A pun is a play on words that's so bad it's good. Like a pizza with extra cheese, but not that kind of cheese, because we're not talking about that kind of cheese.
But seriously, puns are words that sound like one thing but are actually another. Like a 'bass' that sounds like 'base,' or a 'bat' that sounds like 'bait.'
Puns are the highest form of flattery, but not that kind of flattery, because we're not talking about that kind of flattery either. They're just a way of playing with words, like a word game for grown-ups.