The death of a character in a role-playing game is a (usually) permanent end to the character's role in—and contribution to—the ongoing fiction, i.e. the character is no longer played by their player.
Occurrence of death in RPGs[]
A character may die if the character's player (who may be the GM) chooses for it to happen in the story and the death is narrated with the consent of the group. This is most common at the end of a one-shot or at the climax of a campaign.
However, it is far more common in role-playing games for character death to be an extreme form of being taken out, generally as a result of suffering damage, and which can't be undone by means of healing or other recovery. In fact, it is the most common form of being taken out described in role-playing games, especially in games in the action and action-adventure genres. Since death is usually considered to be undesirable, games where it is likely to happen use game mechanics to track it and hold it off, such as hit points and death saves.
For player characters in particular, death can be a very memorable and emotional experience for the character's player. Many game tales, such as "Sameo", revolve around a particularly memorable PC death.
Playing after death[]
Some systems allow a player to continue playing a character even after the character has died. This may be because their character can be resurrected (e.g. by magic or the gods in a fantasy game), or because they can continue playing the character in the afterlife or as a ghost or other form of undead. Alternatively, if a character's death is taken badly, the group can make a ruling to retcon the death. How possible it is to continue playing a character who has died will depend not only on the rules in use but also on the opinions of the group as a whole.
If it is not possible to play the same character after they have died, a player's only choices are to create a new character or stop playing in the campaign.