Why Urvashi has given Arjuna the curse of being impotent? is it true? If yes then what is the reason behind the curse?
Yes, Urvashi cursed Arjuna to lose his manhood. This incident described in Mahabharata, Book 3: Vana Parva: Indralokagamana Parva: SECTION XLVI. When Arjuna was in Indraloka during their exile, he gained all the celestial weapons from Indra. After that Indra asked him to learn music and dance which he learned from Chitrasena, a Gandharva. One day Indra asked Chitrasena that Arjuna has learned everything here so, let him learn how to get acquainted with a woman. So, Indra asked Chitrasena to send Urvashi to the place of Arjuna. Chitrasena told Urvashi about Indra's wish, so she approached Arjuna in night but Arjuna didn't accepted her as lover instead he compared her as mother.
Vaisampayana continued, "While in heaven, hearing her speak in this strain, Arjuna was overcome with bashfulness. And shutting his ears with his hands, he said, 'O blessed lady, fie on my sense of hearing, when thou speakest thus to me. For, O thou of beautiful face, thou art certainly equal in my estimation unto the wife of a superior. Even as Kunti here even this is my wish, and I have cherished it for ever!"
[Some text is obviously missing here--JBH] of high fortune or Sachi the queen of Indra, art thou to me, O auspicious one, of this there is no doubt! That I had gazed particularly at thee, O blessed one, is true. There was a reason for it. I shall truly tell it to thee, O thou of luminous smiles! In the assembly I gazed at thee with eyes expanded in delight, thinking, 'Even this blooming lady is the mother of the Kaurava race.' O blessed Apsara, it behoveth thee not to entertain other feelings towards me, for thou art superior to my superiors, being the parent of my race.'"
But Urvashi told him that Apsaras are free from all these worldly relations.
"Hearing these words of Arjuna, Urvasi answered, saying, 'O son of The chief of the celestials, we Apsaras are free and unconfined in our choice. It behoveth thee not, therefore, to esteem me as thy superior. The sons and grandsons of Puru's race, that have come hither in consequence of ascetic merit do all sport with us, without incurring any sin. Relent, therefore, O hero, it behoveth thee not to send me away. I am burning with desire. I am devoted to thee. Accept me, O thou giver of proper respect.'"
But Arjuna again rejected her argument.
"Arjuna replied, 'O beautiful lady of features perfectly faultless, listen. I truly tell thee. Let the four directions and the transverse directions, let also the gods listen. O sinless one, as Kunti, or Madri, or Sachi, is to me, so art thou, the parent of my race, an object of reverence to me. Return, O thou of the fairest complexion: I bend my head unto thee, and prostrate myself at thy feet. Thou deservest my worship as my own mother; and it behoveth thee to protect me as a son.'"
After that Urvashi became angry and cursed Arjuna as follows:
Vaisampayana continued, "Thus addressed by Partha, Urvasi was deprived of her senses by wrath. Trembling with rage, and contracting her brows, she cursed Arjuna, saying, 'Since thou disregardest a woman come to thy mansion at the command of thy father and of her own motion--a woman, besides, who is pierced by the shafts of Kama, therefore, O Partha, thou shalt have to pass thy time among females unregarded, and as a dancer, and destitute of manhood and scorned as a eunuch.'"
Later, Arjuna told all these to Chitrasena and Chitrasena told to Indra. Indra told Arjuna that this curse will be helpful for him during his Ajnyatavasa (13th year of exile). After that, he will be freed from Urvashi's curse.
In the Critical Edition of the Mahābhārata, there's no story of Urvaśī cursing Arjuna. This is what Bibek Debroy writes in the footnotes to his translation:
Section Thirty-Two - Indralokabhigamana Parva
Indraloka means Indra's world and abhigamana means to go or visit. So this section is about the visit to Indra's world, meaning Arjuna's visit to Indra's world.
Chapter 342 (45)
Vaishampayana said, 'Then knowing Shakra's mind, the gods and the gandharvas welcomed Partha with a supreme arghya. They offered the king's son padya and achamaniya and guided him to the entrance to Purandara's abode. Having been shown such homage, Jishnu lived in his father's house. Pandava learned about all the great weapons and the means of withdrawing them. From Shakra's hands, he received his beloved vajra weapon, impossible to withstand. This made a great roar and was like lightning, marked by the signs of clouds and peacocks. On receiving the weapon, Pandava Kounteya thought of his brothers. But on Purandara's instructions, he lived there happily for five years. When Partha became skilled in the use of all weapons and the right time had come, Shakra told him, "O Kounteya! Now learn singing and dancing from Chitrasena. Learn the music that is only known to the gods and is unknown in the world of men. O Kounteya! If you learn this, it will bring your own welfare." Purandara then gave him to Chitrasena as a friend. Partha lived happily with him, free from all disease.32
32 The critical edition excises some sections that are part of popular renderings of the Mahabharata. That story figures in regional versions and is a story about the apsara Urvashi's desire for Arjuna. Arjuna spurned her because she was like his superior's wife or mother, the Puru dynasty having descended from Urvashi. Urvashi then cursed Arjuna that he would have to live as a woman, bereft of his manhood. Indra reduced the duration of the curse to one year.
Besides, all the five Pāṇḍavas are later granted a boon by Dharma towards the end of the yakṣa-praśna episode to help them live in disguise during the 13th year of their exile. So, this special boon/curse of Arjuna makes no sense.
Chapter 595 (298)
Vaishampayana said, 'At the yaksha's words, the Pandavas stood up. All their hunger and thirst disappeared in an instant.
'Yudhishthira said, "Unvanquished, you are standing on one leg in the lake. I am asking you. Which god are you. I do not think that you are a yaksha. Are you one of the Vasus or one of the Rudras? Are you the foremost among the Maruts? Are you the wielder of the vajra, the lord of the thirty gods? Each of my brothers is capable of fighting hundreds and thousands. I do not see a means whereby all of them can be killed. I see that their senses have been restored and they have awakened pleasantly. Are you our well-wisher or are you our father?" 'The yaksha replied, "O son! O one whose valour is mild! I am your father Dharma. O bull among the Bharata lineage! Know that I arrived with a desire to see you. Fame, truth, self-control, purity, uprightness, humility, steadfastness, charity, austerities and brahmacharya are my body. Know that non-violence, impartiality, peacefulness, austerities, purity and lack of envy are gates towards me. You have always been dear to me. It is fortunate that you are devoted to the five. It is fortunate that you have conquered the six states. Two occur early, two in the middle and two at the end, leading to the hereafter. I am Dharma. O fortunate one! I came here to test you and am satisfied with your non-violence. O unblemished one! I will grant you a boon. O Indra among kings! Ask for a boon. O unblemished one! I will grant it to you. Men who are devoted to me never suffer from misfortune."
'Yudhishthira said, "The deer ran away with his kindling. May his fires not be destroyed. That is the first boon I ask for."
'Dharma replied, "O lord! O Kounteya! In order to test you, I robbed the brahmana of his kindling in the form of a deer."
Vaishampayana said, 'The illustrious one granted him that boon. Then he asked the fortunate one, who was like an immortal, to ask for another boon.
'Yudhishthira said, "The twelve years of dwelling in the forest have passed and the thirteenth has arrived. Wherever we may live, may people not be able to recognize us.
Vaishampayana said, 'The illustrious one granted him that boon. He again comforted Kounteya, for whom truth was his valour. "O descendant of the Bharata lineage! Even if you travel the earth in your own forms, no one in the three worlds will be able to recognize you. O extender of the Kuru lineage! Through my favours, you will spend the thirteenth year, hidden and undetected, in the city of Virata. Whatever form each of you desires to assume in your mind, that will be the disguise you will adopt according to your wishes. Return the kindling to the brahmana, because I stole it in the form of a deer to test you. O son! Ask for a third boon that is great and unmatched. O king! You have been born from me and Vidura has also been born from a part of me." Yudhishthira replied, "O eternal god of the gods! It is sufficient that I have set my eyes on your person. O father! I will happily accept whatever boon you are satisfied to grant me. O lord! May I always be able to conquer avarice, delusion and anger. May my mind always be inclined towards generosity, austerity and truth." Dharma said, "O Pandava! You are naturally endowed with all the qualities. You are dharma yourself. But you will obtain what you ask for." Having said this, the illustrious Dharma, who sustains the worlds, disappeared. The intelligent Pandavas were reunited and slept happily. Freed from exhaustion, all the brave ones returned to the hermitage and gave the kindling to the ascetic brahmana. A self-controlled man who restrains his senses and reads this great account of the restoration and meeting of the father and the son, an account that extends fame, lives for a hundred years with sons and grandsons. Men who know of this good account are never inclined towards adharma and are not separated from their well-wishers. They do not steal the possessions of others or violate other people's wives. They never find pleasure in vile sentiments.'
To give just one more example of this nature, I may recall the incident in which Urvaśī is said to have approached Arjuna during his stay in heaven. The incident is reported in the entire southern recension and only in the Bengali and the Devanāgarī versions of the north, but is absent in the Kashmiri version. We are told that once Indra had noticed Arjuna paying special attention to Urvaśī (pārthasya cakṣur urvaśyāṃ saktaṃ vijñāya vāsāvaḥ). Hence he asked Citrasena to tell Urvaśī to pay a visit to Arjuna one evening. Accordingly she went to Arjuna but he refused to be attracted by her. Enraged, she cursed Arjuna to live like a eunuch. She did not specify the duration of the effect of her curse. When the incident was reported to Indra, he consoled Arjuna by saying that the curse would help him to live like a Bṛhannaḍā during his term of ajñātavāsa. Thus it was Indra who restricted the effect of the curse to one year (3. App. I. no. 6. pp. 1047-1053).
This incident also contradicts a later statement by Arjuna in the Virāṭaparvan. According to it, Arjuna had revealed to Uttara that although he was pretending to be a eunuch, he was really not so. He was only practising a vrata for a year (saṃvatsaram idaṃ vratam / carāmi brahmacaryaṃ vai satyam etad bravīmi te // nāsmi klībo mahābāho .... 4. 40.12-13).