So, there are some clothes that people wear when they are doing special stuff at church. Some people like to wear really fancy and colorful clothes called "vestments" when they do these special things.
But some people think that everyone should be allowed to wear plain clothes when they do these special things, not just the fancy vestments.
So, this is called the "vestments controversy" because some people don't agree on what kind of clothes should be worn during certain religious activities. It's like when you and your friend argue about what game to play, but instead of games, it's about clothes!