to drive out by force: to expel a person or group from a place they would otherwise stay
At its core this verb is forceful removal. Someone with power pushes someone else out, away from a home, a land, a position, or a presence, and the one removed does not go willingly. The same word covers a king driving conquered peoples off their land, a household throwing out an unwanted member, and God expelling the first humans from the garden.
Three shades of that one idea show up in the Bible. Most often it describes clearing nations or people off territory, the language of conquest and dispossession. A second, narrower use is legal: a man putting away his wife, so that a "driven-out woman" is simply the Hebrew term for a divorced woman. A third, vivid use turns the force outward and upward, picturing the restless sea heaving up the mud and filth it cannot keep down.
What ties all three together is the picture of something expelled against the pull that would otherwise hold it in place. People belong to their land, a wife to her household, the sea's silt to its depths, and this verb names the act of forcing them out anyway. The shade you land on depends entirely on what is being driven out and from where.