To keep talking and talking about something, in a way that bores the listener. This is British and informal, and honestly a little old-fashioned now — you hear it more from older British people than from young ones. People say it probably comes from old London rhyming slang ('rabbit and pork' = talk), though few speakers think about that. There is no object: you rabbit on, or you rabbit on ABOUT something.

講個不停、碎碎唸