It can mean two different things I can think of: The first is, if you have fallen behind in a task, "I got a little caught up" means that you did a lot of work, and you're closer to your goal. The analogy there is to a race. The person "catches up" to his or her goal. The second meaning might be that the person got emotionally captured by what they were doing. The analogy is that they have been "caught like a ball" -- they have been "caught" by their emotions or desires. ex. Person 1: "Why did you try so hard to win a casual chess match?" Person 2: "I got a little caught up." [by the chess match] Hope that helps!

Think of being caught up in a fishing net. You can't get out until the net is released. And you have the meaning of this idiom.

It means that you made progress in achieving some goal which is still unfinished. If your are completely caught up, that means that you have finished all tasks that you or someone has assigned you. If you are a little caught up, you have completed part or most of the tasks, but not all.

I got a little catch up is to say that "I am busy"

catch up means be busy working;