Panentheism is the understanding of God as intimately connected to, and yet beyond, the universe we experience. This is distinct from pantheism, which sees the universe as equivalent to God.
Panentheism is an attempt to capture philosophically what the scriptures say about God's pervasive presence. Paul seems to express this idea: "For in him we live and move and have our being".
I have usually understood this as saying that everything emerges from God, in a way similar to icebergs emerging from the ocean. However, this is only an analogy, and not a particularly great one.
Recently, I have backed off on using the term panentheism because it seems to be becoming associated with an impersonal God. Panentheism itself doesn't suggest an impersonal God, so this has been a surprise to me. But given that, it is perhaps not saying enough.