Muck
Muck means to discard your cards face-down into the pile of dead cards, either when you fold or when you give up a hand without showing it.
The muck is the pile of discarded, dead cards sitting in front of the dealer, and "to muck" is the act of sliding your cards into it face-down. Once your cards touch that pile they're dead, you can't get them back, and you've given up any claim to the pot. The word covers both folding during the hand and tossing your cards away at showdown without revealing them.
It comes up in two spots. The first is when you fold to a bet: you push your two hole cards toward the dealer, and that's a muck. The second is at showdown, when an opponent has already shown a hand you can't beat, so you muck instead of exposing your cards, which keeps your bluff or your weak holding private.
For beginners, the simple habit is to wait your turn and slide your cards in face-down rather than flipping them up or tossing them across the table. One thing to know: if you muck at showdown, you forfeit the pot even if your hand was secretly the best one, so when there's any chance you win, turn your cards up instead of mucking. When you do give up a hand, just muck cleanly and quietly rather than reacting or taking your time about it.
Example
You hold 7-2 offsuit on the button, an opponent raises to 3 big blinds, and you fold by sliding your cards face-down to the dealer, that's mucking. Later, on a K-K-9-4-2 board you call the river with A-J, your opponent tables K-Q for trip kings, and rather than show your busted hand you simply muck.