Dead stones are stones that cannot live or cannot have two eyes, pretty much. For example, if player A has some stones inside of player B's territory, and A's stones can't make two eyes, then those stones would be considered dead, and they would count towards B's score at the end of the game.
As to why you can mark safe groups dead in FOD, is because the computer can't do it for you, so you have to manually select each dead stone(s). This can be a bit troublesome at times, since some players try to waste time, but be patient and they'll give up eventually. ^^