Literally the word signifies anything that is not kṣara, not destructible, hence imperishable. The Upaniṣads use it to describe Brahman or even as its synonym. For example: Bṛhadāraṇyaka 3.8.8, 9, 10 and 11; Kaṭha 3.2; Muṇḍaka 1.1.5; 2.2.2 and so on. It is for this reason that the Hindu mythology uses the word as one of the many names of Śiva and Viṣṇu.
Akṣara also signifies Praṇava or Om, the monosyllable that stands for the highest Brahman (vide Bhagavadgītā 8.13).
The word is also widely used to indicate the letters of the Sanskrit alphabet.