1. Literally, to rub against someone or something in an intense or persistent manner. The girl I started dating has a dog that rubs up on me whenever I go over to her house. The elephant started rubbing up on our jeep, making me nervous that it would tip us over.

2. To refamiliarize oneself with or stimulate one's memory about a topic or issue. I need to rub up on factorials before attempting to teach them on Monday. I'm spending the weekend rubbing up on Japanese before we fly to Tokyo on Monday.