It's important to provide some background to begin this talk, after which we talk of kalās and kalādhva. I presume you are familiar with 36 tattvas in Śaivism which is unlike Vedānta that has only 25 tattvas, if not familiar (see Lakshmanjoo, 2003, pg. 1-10 ).
The common meaning of adhvan is path or road (mārga). In the context of Śaivism it is usually interpreted as path, adhvā yātavyamārgaḥ (an adhvan is a road to destination, Svāyambhuvāgama III.7a). Sadyojyoti defines it (Ibid. III.11): yatra pādaviharaṇākhyaṁ krama krameṇa dr̥ṣṭaṁ so 'dhvā loke prasiddhāḥ i.e. 'that in which the action called walking is seen with sequence, is well known as adhvan'.
Dīkṣā refers to the final cutting of material bonds to attain mokṣa or nirvāṇa, which is only possible with the grace of a guru. (Svāyambhuvāgama I.16-19). There are three bonds: mala, karman, māyā. Although dīkṣa is theoretically defined the removal of three bonds, but practically it only deals with the elimination of karman and māyā, while the removal of mala is just a consequence. (see Kriyāpada VII.86-88, Mr̥gendrāgama). Dīkṣa thus appears the enactment of the consummation of karman in the midst of māyā. Practically, the guru ties a string (sūtra) to tuft of hair (śikhā) of the disciple. The self of the disciple, his/her karman, the totality of māyā (with it's pure extension called bindu) have been placed ceremonially on the string and in several manners. This is the basis of the concept of adhvans. An adhvan is a representation of māyā bindu and it is necessary to make sure that nothing of it is left over, in order to ensure that the operation of dīkṣa is complete and successful.
The objective universe is said to be threefold, being composed of three paths (adhvans). These adhvans are gross (sthūla), subtle (sūkṣma) and subtlest (para). The gross path is called bhuvanādhva (path of all worlds), the subtle path is called tattvādhvaa (path of all tattvas) and the subtlest path kalādhva (path of all kalās). These are the basic 3 adhvans, there are actually six adhvans in Śaiva-Siddhānta (other ones are varṇādhva, mantrādhva, vyomavyāpimantrādhva which we won't cover here)
Bhuvanādhva is a combination of 118 worlds (bhuvanas) like this cosmos which have been created. Tattvādhva is the complete system of 36 tattvas.
Kalādhva is a more subtlest adhvan (path) of these three. It consists of 5 kalās which are 5 boundaries or enclosures. These kalās are enclosure for all 36 tattvas. The first and outermost enclosure is called nivr̥tti kalā, in which the pr̥thvi tattva is enclosed. In the next kalā, pratiṣṭhā kalā, there are 23 tattvas enclosed from jala tattva to prakr̥ti tattva. The next enclosure is vidyā kalā, which consists of 7 tattvas, from puruṣa tattva upto and including māyā tattva. In the next enclosure, śāntā kalā, there are 4 tattvas from śuddhavidyā tattva upto and including śakti tattva enclosed. The fifth and last enclosure, śāntātitā kalā, encloses the śiva tattva. Śāntātitā kalā is found in this bindu āvṛiti, in that one-pointed established state of bindu, point.
These five kalās together are the pure form of māyā i.e. bindu. Each of these are related to śaktis of Śiva having definite functions. The concept of these functions is defined as follows: (Vidyāpada, Mr̥gendrāgama)
karotya unmīlanaṁ yābhiḥ śaktibhir naratejasaḥ |
tā nivr̥ttyādi saṁjñānāṁ bhuvanānāṁ adhīśvarāḥ || 166 ||
The śaktis by which Śiva oppens the light of (consciousness of) the Self are the Lord of worlds called nivr̥tti, etc.
Here, we see the worlds which are transformations of māyā and bindu are grouped under five heads which are the kalās i.e. nivr̥tti etc. Each group is ruled by a Lord who is a śakti of Śiva. These five śaktis have a common character, which is to contribute to the awakening of the powers of knowledge and action of Self, and thus to contribute to the attainment of their goal. Kalās, in this way serve as an appropriate base for the operation of dīkṣā. Their respective function is as follows in the Vidyāpada of Mr̥gendrāgama, which illustrates well the hierarchy and the names of kalās in relation to the attainment of liberation:
nivartayati bhūtāni yayā sāsya nivartikā |
nivr̥ttir iti tatsthānaṁ tatreśo 'pi nivr̥ttimān || 167 ||
nivr̥ttasya gatir bhūyo yayā pracyāvalakṣaṇā |
niṣidhyate pratiṣṭhā sā shtānaṁ tadvāṁś ca tatpatiḥ || 168 ||
tyaktvāptagamyaviṣayaṁ yayā jñānaṁ dadāty aṇoḥ |
sā vidyā sthānam apy asyā vidyeśaś ca tadīśvaraḥ || 169 ||
sarvaduḥkhapraśamanaṁ yayāsya kurute haraḥ |
sā śāntis tatpadaṁ ceti tat kurvan so 'pi śāntimān ||170 ||
The [śakti] by which [Śiva] checks the creation of elements and living species, is the checking power; the place where it occurs is called 'check[-point]' (nivr̥tti), and the Lord [Śiva considered] in this place is called 'possessor of nivr̥tti'
The [śakti of Śiva] by which the fall of the checked soul [into lower births] is suppressed is the 'stabilizing power' (pratiṣṭhā); its location [is called 'stabilization' (pratiṣṭhā)], and the Lord over it is the 'possessor of pratiṣṭhā'
The [śakti] by which [Śiva] gives the Self a knowledge, the contents of which do not come from śābda (verbal testimony) or anumāna (inference), is the 'power giving direct experience' (vidyā); its location [is called 'place of direct experience'], and the Lord over it is the 'Lord of vidyā'
The [śakti] by which Hara achieves the pacification of all the sufferings of the soul is the 'pacification' (śānti); its location is called 'place of pacification', and the Lord who accomplishes it is 'possessor of śānti'
This passage of Mr̥gendrāgama deals only with the above-mentioned 4 kalās. There is fifth one, which we stated before, known as śāntātitā or śantyatīta (beyond śānti), easily identifiable as the supreme Śakti of Śiva (Śiva himself in the context of Kashmir Śaivism) and Mr̥gendrāgama itself qualifies it in the context of dīkṣa as bindu. (Kriyāpada VII.83, Mr̥gendrāgama).
Lakshmanjoo (2003). Thirty-Six Elements: Tattvas . In J. Hughes (ed.). Kashmir Shaivism : The Secret Supreme. (pp. 1-9). Ishwar Ashram Trust
Lakshmanjoo (2003). The Sixfold Path of the Universe: Ṣaḍadhvan . In J. Hughes (ed.). Kashmir Shaivism : The Secret Supreme. (pp. 11-13). Ishwar Ashram Trust
Filliozat, P.S. (1994). The Concept of Adhvan in Śaivasiddhānta. Wiener Zeitschrift Für Die Kunde Südasiens / Vienna Journal of South Asian Studies, 38, 421–433. http://www.jstor.org/stable/24007350