Ready to, on the verge of, as in I was about to leave when it began to rain, or He hasn't finished yet but he's about to. This usage was first recorded in Miles Coverdale's 1535 translation of the Bible (Joshua 18:8).
not about to. Having no intention of doing something, as in The shop steward was not about to cross the picket line, or Are you staying longer?—No, I'm not about to. [Colloquial; first half of 1900s]