When you smudge something, you smear or blur it in a messy way. If you smudge your sister's drawing after she worked so hard on it, she'll be furious.
You might smudge dirt across your face when you wipe your nose after digging in the garden—and the dirty mark itself can also be called a smudge. Another kind of smudge is a smoky fire that can be used for several purposes: to disguise your location, to keep outdoor plants or trees warm, or to repel insects. The container in which a smudge is built is called a smudge pot.