I've read about Bharatavarsha in many books, but only found the origin of the term Bharatavarsha. Is there a description of Bharatavarsha (i.e., what constitutes Bharatavarsha), in a holy book?
You said you already know the origin of the name Bharata Varsha, but for those who don't, the reason the Indian subcontinent is called Bharata Varsha is because it was conquered by the empire of the ancient king Bharata, as described in the Srimad Bhagavatam:
Formerly this [land] was known as Ajanābha-varṣa, but since Mahārāja Bharata’s reign it has become known as Bhārata-varṣa.
The Bharata referenced in the Srimad Bhagavatam was the son of Rishabha, the founder of Jainism. But more recently India may have been named after another Bharata, who was the son of the king Dushyanta and Shakuntala, daughter of the sage Vishwamitra. (Shakuntala was a product of Vishwamitra's dalliance with the Apsara Menaka, which is described in this chapter of the Bala Kanda of the Ramayana.) Note that Bharata didn't do all the conquests; the Bharata dynasty only solidified its control after the Battle of Ten Kings, which I discuss here.
In any case, to answer your question, yes, there are numerous scriptures which contain descriptions of the labs of Bharata Varsha:
Here is how the Srimad Bhagavatam describes Bharata Varsha:
In the tract of land known as Bhārata-varṣa, as in Ilāvṛta-varṣa, there are many mountains and rivers. Some of the mountains are known as Malaya, Maṅgala-prastha, Maināka, Trikūṭa, Ṛṣabha, Kūṭaka, Kollaka, Sahya, Devagiri, Ṛṣyamūka, Śrī-śaila, Veṅkaṭa, Mahendra, Vāridhāra, Vindhya, Śuktimān, Ṛkṣagiri, Pāriyātra, Droṇa, Citrakūṭa, Govardhana, Raivataka, Kakubha, Nīla, Gokāmukha, Indrakīla and Kāmagiri. Besides these, there are many other hills, with many large and small rivers flowing from their slopes. Two of the rivers — the Brahmaputra and the Śoṇa — are called nadas, or main rivers. These are other great rivers that are very prominent: Candravasā, Tāmraparṇī, Avaṭodā, Kṛtamālā, Vaihāyasī, Kāverī, Veṇī, Payasvinī, Śarkarāvartā, Tuṅgabhadrā, Kṛṣṇāveṇyā, Bhīmarathī, Godāvarī, Nirvindhyā, Payoṣṇī, Tāpī, Revā, Surasā, Narmadā, Carmaṇvatī, Mahānadī, Vedasmṛti, Ṛṣikulyā, Trisāmā, Kauśikī, Mandākinī, Yamunā, Sarasvatī, Dṛṣadvatī, Gomatī, Sarayū, Rodhasvatī, Saptavatī, Suṣomā, Śatadrū, Candrabhāgā, Marudvṛdhā, Vitastā, Asiknī and Viśvā. The inhabitants of Bhārata-varṣa are purified because they always remember these rivers. Sometimes they chant the names of these rivers as mantras, and sometimes they go directly to the rivers to touch them and bathe in them. Thus the inhabitants of Bhārata-varṣa become purified.
The people who take birth in this tract of land are divided according to the qualities of material nature — the modes of goodness [sattva-guṇa], passion [rajo-guṇa], and ignorance [tamo-guṇa]. Some of them are born as exalted personalities, some are ordinary human beings, and some are extremely abominable, for in Bhārata-varṣa one takes birth exactly according to one’s past karma. If one’s position is ascertained by a bona fide spiritual master and one is properly trained to engage in the service of Lord Viṣṇu according to the four social divisions [brāhmaṇa, kṣatriya, vaiśya and śūdra] and the four spiritual divisions [brahmacārī, gṛhastha, vānaprastha and sannyāsa], one’s life becomes perfect.
This chapter of the Vishnu Purana contains a similar description to that of the Srimad Bhagavatam:
In the Bhárata-varsha it is that the succession of four Yugas, or ages, the Krita, the Treta, the Dwápara, and Kali, takes place; that pious ascetics engage in rigorous penance; that devout men offer sacrifices; and that gifts are distributed; all for the sake of another world. In Jambu-dwípa, Vishńu, consisting of sacrifice, is worshipped, as the male of sacrificial rites, with sacrificial ceremonies: he is adored under other forms elsewhere. Bhárata is therefore the best of the divisions of Jambu-dwípa, because it is the land of works: the others are places of enjoyment alone. It is only after many thousand births, and the aggregation of much merit, that living beings are sometimes born in Bhárata as men. The gods themselves exclaim, "Happy are those who are born, even from the condition of gods, as men in Bhárata-varsha, as that is the way to the pleasures of Paradise, or the greater blessing of final liberation. Happy are they who, consigning all the unheeded rewards of their acts to the supreme and eternal Vishńu, obtain existence in that land of works, as their path to him. We know not, when the acts that have obtained us heaven shall have been fully recompensed 7, where we shall renew corporeal confinement; but we know that those men are fortunate who are born with perfect faculties 8 in Bhárata-varsha.
Here is how Sanjaya describes Bharata Varsha to Dhritarashtra in the Bhishma Parva of the Mahabharata:
I will now, O chastiser of foes, describe to thee that country as I have heard of it. Listen to me, O king, as I speak of what thou hast asked me. Mahendra, Malaya, Sahya, Suktimat, Rakshavat, Vindhya, and Paripatra,--these seven are the Kala-mountains 1 (of Bharatvarsha). Besides these, O king, there are thousands of mountains that are unknown, of hard make, huge, and having excellent valleys. Besides these there are many other smaller mountains inhabited by barbarous tribes. Aryans and Mlecchas, O Kauravya, and many races, O lord, mixed of the two elements, drink the waters of the following rivers, viz., magnificent Ganga, Sindhu, and Saraswati; of Godavari, and Narmada, and the large river called Yamuna... and Mandakini, and Supunya, Sarvasanga, O Bharata, are all mothers of the universe and productive of great merit. Besides these, there are rivers, by hundreds and thousands, that are not known (by names), I have now recounted to thee, O king, all the rivers as far as I remember.
After this, listen to the names of the provinces as I mention them. They are the Kuru-Panchalas, the Salwas, the Madreyas, the Jangalas, the Surasena, the Kalingas, the Vodhas, the Malas, the Matsyas, the Sauvalyas, the Kuntalas, the Kasi-kosalas, the Chedis, the Karushas, the Bhojas, the Sindhus, the Pulindakas, the Uttamas, the Dasarnas, the Mekalas, the Utkalas; the Panchalas, the Kausijas, the Nikarprishthas, Dhurandharas; the Sodhas, the Madrabhujingas, the Kasis, and the further-Kasis; the Jatharas, the Kukuras, O Bharata; the Kuntis, the Avantis, and the further-Kuntis; the Gomantas, the Mandakas, the Shandas, the Vidarbhas, the Rupavahikas; the Aswakas, the Pansurashtras, the Goparashtras, and the Karityas; the Adhirjayas, the Kuladyas, the Mallarashtras, the Keralas, the Varatrasyas, the Apavahas, the Chakras, the Vakratapas, the Sakas; the Videhas, the Magadhas, the Swakshas, the Malayas, the Vijayas, the Angas, the Vangas, the Kalingas, the Yakrillomans; the Mallas, the Suddellas, the Pranradas, the Mahikas, the Sasikas; the Valhikas, the Vatadhanas, the Abhiras, the Kalajoshakas; the Aparantas, the Parantas, the Pahnabhas, the Charmamandalas; the Atavisikharas, the Mahabhutas, O sire; the Upavrittas, the Anupavrittas, the Surashatras, Kekayas; the Kutas, the Maheyas, the Kakshas, the Samudranishkutas; the Andhras, and, O king, many hilly tribes, and many tribes residing on lands laying at the foot of the hills, and the Angamalajas, and the Manavanjakas; the Pravisheyas, and the Bhargavas, O king; the Pundras, the Bhargas, the Kiratas, the Sudeshnas, and the Yamunas, the Sakas, the Nishadhas, the Anartas, the Nairitas, the Durgalas, the Pratimasyas, the Kuntalas, and the Kusalas; the Tiragrahas, the Ijakas, the Kanyakagunas, the Tilabharas, the Samiras, the Madhumattas, the Sukandakas; the Kasmiras, the Sindhusauviras, the Gandharvas, and the Darsakas; the Abhisaras, the Utulas, the Saivalas, and the Valhikas; the Darvis, the Vanavadarvas, the Vatagas, the Amarathas, and the Uragas; the Vahuvadhas, the Kauravyas, the Sudamanas, the Sumalikas; the Vadhras, the Karishakas, the Kalindas, and the Upatyakas; the Vatayanas, the Romanas, and the Kusavindas; the Kacchas, the Gopalkacchas, the Kuruvarnakas; the Kiratas, the Varvasas, the Siddhas, the Vaidehas, and the Tamraliptas; the Aundras, the Paundras, the Saisikatas, and the Parvatiyas, O sire.
There are other kingdoms, O bull of Bharata's race, in the south. They are the Dravidas, the Keralas, the Prachyas, the Mushikas, and the Vanavashikas; the Karanatakas, the Mahishakas, the Vikalpas, and also the Mushakas; the Jhillikas, the Kuntalas, the Saunridas, and the Nalakananas; the Kankutakas, the Cholas, and the Malavayakas; the Samangas, the Kanakas, the Kukkuras, and the Angara-marishas; the Samangas, the Karakas, the Kukuras, the Angaras, the Marishas: the Dhwajinis, the Utsavas, the Sanketas, the Trigartas, and the Salwasena; the Vakas, the Kokarakas, the Pashtris, and the Lamavegavasas; the Vindhyachulakas, the Pulindas, and the Valkalas; the Malavas, the Vallavas, the further-Vallavas, the Kulindas, the Kalavas, the Kuntaukas, and the Karatas; the Mrishakas, the Tanavalas, the Saniyas; the Alidas, the Pasivatas, the Tanayas, and the Sulanyas; the Rishikas, the Vidarbhas, the Kakas, the Tanganas, and the further-Tanganas. Among the tribes of the north are the Mlecchas, and the Kruras, O best of the Bharatas; the Yavanas, the Chinas, the Kamvojas, the Darunas, and many Mleccha tribes; the Sukritvahas, the Kulatthas, the Hunas, and the Parasikas; the Ramanas, and the Dasamalikas. These countries are, besides, the abodes of many Kshatriya, Vaisya, and Sudra tribes. Then again there are the Sudra-abhiras, the Dardas, the Kasmiras, and the Pattis; the Khasiras; the Atreyas, the Bharadwajas, the Stanaposhikas, the Poshakas, the Kalingas, and diverse tribes of Kiratas; the Tomaras, the Hansamargas, and the Karamanjakas. These and other kingdoms are on the east and on the north.
Whew! That's what I call thorough knowledge of geography.
Definition of Bharatvarsh By The Vedik Foundation:
According to the scriptural description of the brahmand the entire earth planet is called Bharatvarsh, but particularly the area of the continent that lies south of the Himalayas is called Bharatvarsh. It is also called Aryavart. The inhabitants of Aryavart are called the Aryans as referred to in the Rigved. Thus, the words Bhartiya or Aryans were both used for the inhabitants of Bharatvarsh or Aryavart, however, the words Bharatiya and Bharatvarsh were more popular.
Here is what agnideva says in the chapter 118th Description of Bharatvarsha in AgniPurana:-
Agnideva Says :-
The country situated in the north of sea and south of Himlayas is called Bharat.Area of that country is about nine thousand Yojans (45 thousand kilometers).This is Karmabhumi(Workplace) for the people with wishes of Swarg(Heaven) and Apwarg. Mahendra,Malay,Sahya,Shuktiman,Himalay,Vindhya and Pariyatra,These are total seven Paravat here.IndraDeep,Kasheru,Tamrawarn Gabhastiman,Nagdeep,Soumya,Gandhrav and Warun these are eight islands here.Bharat is the ninth island surrounded by sea.Bharat island is thousands of killometer long from south to north. Bharat have nine parts.Bharat island is situated in the middle.In it Kirats are in the easterns side and yamans are in the western side. Middle of Bharat island is for Brahmans and similar casts. From Pariyatra Hill rivers like Veda-Smriti are generated.From Vindhyanchal Hill rivers like Narmada are generated.From Sahya Hill Tapti,Payoshni,Godavari,Bheemrathi and Krishnaveta rivers are generated. From Malay rivers like Kritmasa and From Mahendra Rivers like Trimasa are generate d.From Suktiman rivers like Kumari and From Himalaya rivers like chandrabhaga are generated.In the west part of Bharat island Kuru,Panchal and Madhyadesh are situated.