It means that if you miss a "green in regulation" (i.e., you are not on the green in par minus 2), but you still make par or better on the hole.
Up = chipping/pitching/hitting onto the green
Down = putting into the hole.
However, it still counts as an "Up and Down" if you hole out from chip/pitch/approach.
A "sand save" is the same thing, but from a greenside bunker.