The Playground of Souls
Līlāvibhūti (also called karma-bhūmi or the realm of action) is this cosmos — the fourteen worlds (bhuvana) from the lower realms to Brahmā's abode (Brahmaloka). Unlike nityavibhūti, this realm is transient (anitya): it undergoes periodic dissolution (pralaya) and re-creation. Its matter is the three-guṇa prakṛti — the substance of māyā that binds souls.
Why It Is Called Līlā
The term līlā (divine sport or play) is not trivial — it conveys that the Lord creates and dissolves this cosmos not out of necessity (he lacks nothing) but out of his divine spontaneity, his overflowing joy, his compassion to give souls a field in which to work out their karma and seek liberation. It is his play in the sense that nothing in it can diminish him or add to him.
Bound Souls in Līlāvibhūti
In līlāvibhūti, the baddha-jīvas (bound souls) cycle through birth and death, experiencing the fruits of their karma under the influence of beginningless avidyā (ignorance). The Bhagavad Gītā and the Upaniṣads are all addressed to souls in this realm, pointing them toward the way out (upāya) — toward liberation and the attainment of nityavibhūti.
Relationship to the Lord
Even in līlāvibhūti, the Lord is fully present — as antaryāmī (inner controller), as the avatāras (descended forms), as the arcā-vigraha (deity in temples). The Lord does not abandon this realm; he is its sustainer and its redeemer.