Vahni-maṇḍala-vāsinī वह्नि-मण्डल-वासिनी (352)

She lives in the sphere of fire. Vahni means fire. The sphere of fire is said to be in mūlādhāra cakra and in ākāś or ether.  Already nāma 99 mūlādhārika nilaya explained that She resides in the base cakra. The other interpretation that She resides in ākāś is based on the saying that agni prevails in ether as well. Vahni also means numeric three. This numeric three could mean the moon, the sun and the fire one below the other in the spine. The moon is in sahasrāra, the sun in anāhata and the fire in mūlādhāra. She is in the form all these three. The Pañcadaśī mantra consists of three kūṭa-s and this nāma could mean that She resides in this mantra. Possibly this could be the reason why Pañcadaśī mantra is considered as the supreme mantra

Bhaktimat-kalpa-latikā भक्तिमत्-कल्प-लतिका (353)

Kalpa is a divine creeper that grants boon to those who sit under it.  In the same way She gives boon to Her devotees. Latika means spread over. This indicates that Her devotees are spread over across the earth (devotees is a general term representing the whole humanity).  Kalpa also means imperfection. Those who worship Her with imperfect devotion are made to acquire perfect devotion over several births and She gives them final liberation. There is difference between final liberation and reaching the Heavens which is called mokṣa. The final liberation means no re-birth and mokṣa means after exhausting all good karma-s in the Heaven (the heaven can be explained as a place where certain souls are rested for some period of time). Other souls are reborn immediately after leaving a body. The soul reaching the Heaven, does not attain perfection to become eligible to get liberated.  Such final salvation is possible only with Her grace. This is the inherent meaning of this nāma. 

Kṛṣṇa says (Bhagavad Gīta XV.10) “The yogis striving for liberation see Him existing in themselves; but those who are un-purified and undisciplined are unable to perceive Him even when they struggle to do so.”

Paśu-pāśa-vimocanī पशु-पाश-विमोचनी (354)

The concept of self-realization is best explained in Bṛhadāraṇyaka Upaniṣad (I.iv.10). It says “This self was indeed Brahman in the beginning.  It knew only Itself as, ‘I am Brahman.’  Therefore, It became all. And whoever among the gods knew It also became That; and the same with sages and men.” When one realizes the Brahman, he becomes everything. Those who do not have the requisite knowledge to know the Brahman are called paśu-sPaśu generally means cattle; but in the present context it can be explained as the individual soul as distinct from the divine Soul of the universe. In other words, paśu here means those who do not possess knowledge about the Brahman. Pāśa means bondage arising out of ignorance. The cattle need just food and beyond food they do not think about anything, because they are incapable of thinking. That is why those who do not possess wisdom for knowing the Brahman are called paśu-s.

Liṅga Purāṇa says paśu-s are the individual souls and pāśa is the bondage and such bondage of paśu-s are destroyed by Paśupatī, the Lord of all paśu-s (Śiva).

It is better to know a little more on paśu as this word is more frequently used in many UpaniṣadsŚiva Sutra I.2 says jñānam bandhaḥJñānam means vitiated knowledge and bandhaḥ means bondage. Limited knowledge is ignorance.  Ignorance is the cause for bondage that veils the true Brahman. This phenomenon is called āṇava mala. Mala has been explained as ignorance that hampers the free expression of the Brahman.  Āṇava mala means innate ignorance of the soul. Āṇava is the word derived from the root aṇu which means the empirical individual.  This āṇava mala   is subdivided into two. The first one is the ignorance innate in the very being of the individual Self and other is ignorance inherent in the intellect or buddhi. The āṇava mala is the cause of bondage. Those who are afflicted by such āṇava mala undergo birth and death. This nāma says that She removes this āṇava mala for Her devotees, which is a precondition for final liberation.