In general it refers to God's property of being self-existent. By way of background, I provide the following explanation:
By self-existence we mean
(a) That God is "causa sui," having the ground of his existence in himself. Every being must have the ground of its existence either in or out of itself. We have the ground of our existence outside of us. God is not thus dependent. He is a se; hence we speak of the aseity of God.
But lest this should be be misconstrued, we add
(b) That God exists by the necessity of his own being. It is his nature to be. Hence the existence of God is not a contingent but a necessary existence. It is grounded, not in his volitions, but in his nature.
Augustus Hopkins Strong, Outlines of Systematic Theology, p. 72 1908 ed.