Apara is a name of Śiva-Mahādeva (Siva-Mahadeva). ‘Para’ means ‘other’, it also means the best or the greatest. In Upaniṣad (Upanishad), while describing the nature of Parameśvara (Parameswara; the Supreme Self), it is said that there is nothing better than Him, nothing greater than Him, or nothing more subtle than Him. The entire universe is pervaded by that Supreme Self —
yasmāt paraṃ nāparamasti kiñcit
yasmannāṇīyo na jyāyo’sti kiñcit.
vṛkṣa iva stavdho divi tiṣṭhotyeka
stenedaṃ pūrṇaṃ puruṣeṇa sarvam.
According to this concept of Upaniṣad, there is nothing better or greater than, or even equal to Parameśvara Śiva — so He is known as Apara.