Permadeath (short for permanent death) is one of the main features of roguelikes. It consists in the fact that once your character dies in the game, you can't restore him to a previous status via save-files or save-states. This means that once your character dies, he is dead for good.
Although the feature is commonly reffered to as "Permadeath", it applies not only to death: whatever bad (or good) thing happens to your character, you cannot go back in time. (One exception: roguelikes should allow the player to restore character if the game crashes due to a bug or external reason.)
The idea may scare people from other RPG genres, such as console and common "plot" RPGs, as it is common custom to reload the game after something bad happens to the main character or his party; however, this feature makes roguelikes unique, demanding all your attention and thinking your best moves because the life of your character must be kept.
Permadeath is not as horrible as it might sound at first. The design of roguelikes is built around this concept. This is one of the reasons why they tend to be light in plot. Unlike an RPG, where starting over can involve doing the same hundred page conversation over again, a roguelike presents you with fresh challenges every game. Some other traditional roguelike features, like hidden traps and requirement to identify potions, also make more sense with permadeath.
Of course, roguelikes have saving facilities that allow long games to be played for several days, weeks or even months; but the save-file is deleted upon the death of the character.
The Permadeath can easily be avoided via backup of save files, however this is widely considered as cheating, and not the right way of playing the games. Using backups of save files is known as Savescumming.