1. To learn about something that one missed when it originally happened. In this usage, a noun or pronoun can be used between "catch" and "up." If you haven't been watching the news for the last few days, you have a lot to catch up on. I need to catch up on all the gossip! I'm sure I missed a lot over spring break.

2. To do a task that one has neglected. If you haven't done any biology homework in weeks, you better spend this weekend catching up on it—it's due on Tuesday! I'm trying to catch up on work after being out sick, but my inbox alone might take all day!