The basic doctrine of the aseity of God is that God is wholly independent of his creation. God's creation is dependent upon Him. God is wholly complete without His creation. So for example, while God delights in His creation, His creation doesn't "complete Him" or "fulfill Him" whether emotionally or metaphysically.
God's aseity is one of the foundational doctrines upon which other doctrines are built. Like the Trinity, the doctrine of aseity is indispensable to all of our theological thinking. Even more, it is important for worship. God alone is self-sufficient in Himself. We come to Him as the dependents coming to the Independent One.
Consider K. Scott Oliphint:
"The aseity of God, therefore must be the place on which we stand in order to assert anything else about him, given that anything else we say about him depends for its proper understanding and meaning on that aseity. Or, to put it a bit more succinctly, unless God is a se (of himself), he is not God, and no characterization of God that excludes this aseity can be true of him. Any theology that denies of otherwise negates this aseity cannot be sustained as a true, biblical doctrine of God. A god who is not a se, and thus who is essentially dependent, is a god who is unable to be god. In order for God to be who he is, he must be and remain essentially independent." [God With Us, p. 19]