As others have mentioned, God being the "Ground of all Being" is usually said in reference to God being the efficient cause of all contingent being. Everything that exists is dependent on God, and nothing exists that is independent of Him. In short, God created and sustains the universe.
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It is a phrase primarily used by mystics to describe the "." However, to understand this conceptually, you'll have to remove this idea you have about God as an entity. In Buddhism, this experience is referred to as sunyata. This word literally means voidness, but it doesn't mean voidness in the sense of nothing, of just negative. It means voidness in the sense of "ultimate consciousness." You see, if you would consider what sort of impression would God have of himself? In the eastern view, God obviously wouldn't look at his hands, like we do, and see he's an old man with a beard sitting on a throne. It's instead God as the kind of ultimate, ultimate, then which there is no whicher, outside which there is nothing, which has no edges. He wouldn't therefore look like a ball, he wouldn't like a cube, he wouldn't look like a body, there would be no way at all of conceiving the final self of all Selves. So, that's why it's represented as voidness, as total transparency, as a kind of ultimate space in which everything can happen. This is the "ground of all being," and this is not the imagined anthropomorphized conception of God as entity, but rather a concept transduced from this religious experience where this colossal phenomenon is intuited within the experience itself.