1. Literally, to swim (in something or some place) aimlessly or from place to place. We spent the whole afternoon swimming around in the lake by the cabin. The water in the pool is shallow enough that kids can just swim around on their own.

2. To flit around (in something or some place) very quickly or intangibly. I had so many people's names swimming around in my head by the end of the evening that I couldn't keep any of them straight. There are some rumors swimming around that the company is going to start laying people off.