A mess is a generally dirty state, like your bedroom, your hair, or anything else that's untidy. If you make a huge mess when you cook, you probably try to get someone else to do the clean-up.
In addition to describing a jumble of stuff, mess can describe a confused or difficult situation, like the mess your finances are in if you have seven credit cards. When you mess something up, you cause disorder and maybe even wreck something, like a friendship you messed up by gossiping. And you might eat in a mess hall, a cafeteria for members of the armed forces — and it's probably very neat and orderly, not messy.