Things that aren't clean are dirty. The greasy pans in your sink, your muddy shoes, your smelly dog, your strange uncle's jokes — all of these things are dirty.
When your car is dirty, you should to take it to the car wash, and when your hands are dirty, you need to be sure to wash them with soap and warm water. Some jobs are dirty, like mining, farming, and ditch digging, and the adjective dirty is sometimes used to mean "contaminating" or "poisonous," as with "dirty bombs." If you call your friend a "dirty rat," you mean to let him know you're disgusted with him.