Mucking your hand means that you are discarding your cards so they are not shown at the table -- instead they go into what's called the "muck pile" containing all of the discarded cards from that hand. A muck is different from a fold because the cards are still in play, they just aren't shown to the other players at the table.
On Replay Poker, this is an optional setting that can be changed in your account settings here: http://www.replaypoker.com/settings if you would prefer to show your cards during all showdowns. To show all of your cards during showdown rather than mucking, uncheck the Auto Muck box.
Otherwise, the default is to muck your cards in the following situations:
- If you lose during a showdown and you were not the last person to take aggressive betting action at the table (e.g. I make a bet after the river card, you call, I have the better hand at the showdown, so your cards are mucked and not shown).
- If all the other players fold before the end of a hand.