This is a center cap for a Honda wheel. The specific car this is on is a Honda Fit, but those rims tend to be common on other cars as well. This piece is made to cover the center part of the wheel mounting area and prevent water from sitting in there and rusting things out (these are on my winter tires).
It is a very tight fit, but it's needed for the part to stay on. Scale the part down a bit if you want to have a looser fit. I installed mine by using a rubber mallet. You won't need to remove these from the wheel for any reason, so it doesn't matter that they don't come out easily. If you want to remove them, I'd recommend taking the wheel off and hammering it out from the backside of the rim.
I was tempted to add a fun design to them, but I'll leave that as an exercise to the reader.