Smug means having an annoying kind of satisfaction with yourself, showing it in a way that suggests you think you're better or smarter than others. When someone acts smug, they wear a self-satisfied expression that says, “I'm so clever” or “I knew I was right all along.”

Picture a classmate who solves a math problem first, then sits back with a superior smile, arms crossed, clearly thinking about how brilliant they are rather than simply feeling pleased with their work. That's smugness. Or imagine someone who predicted their team would win, and when they do, they can't stop reminding everyone about their prediction, acting like it proves they're wiser than everyone else.

The word carries a negative feeling because smug people are focused on their own superiority rather than genuine accomplishment. There's a difference between feeling proud of real achievement and feeling smug: pride recognizes an accomplishment, while smugness is about feeling better than other people. A smug person often annoys others because their satisfaction comes with an unspoken “and you're not as good as me” attached to it.

You might describe someone's expression as a smug grin or smug smile, the kind that makes you want to prove them wrong.