Simple Definition:

A pet peeve is something that annoys or bothers someone. It can be a specific action, behavior, or habit that triggers a negative reaction [makes them feel annoyed or upset]. For example, someone’s pet peeve may be when people chew loudly, interrupt them while they’re speaking, or leave dirty dishes in the sink.

Very Simple Definition:

A pet peeve is something that really bothers someone. For example, it can be when people make loud chewing sounds, interrupt when others are speaking, or leave dirty dishes in the sink.