You've already learned that 口 means "mouth" and here it's followed by the particle に, which pinpoints a location. The verb する means "to do" so you're doing something to your mouth! Logically enough, this expression is used to describe lots of actions that you do with your mouth. It's often used to mean to mention or to say, but with an added descriptive nuance that you've said something accidentally or unexpectedly, maybe something you shouldn't have said! 🙊

It can also mean other things done with the mouth, like to eat and to drink!