Short answers, pulled from the story.
A saved game is a piece of digitally stored information about a player's progress in a video game. It allows players to stop and resume play without starting over, and is common in virtually all modern video games, especially role-playing games.
Taito's 1978 shoot 'em up Space Invaders was the first game to save the player's score. For console game progress saves, Pop and Chips for the Super Cassette Vision in 1985 was the first, using an AA battery on the game cassette.
Permadeath, also called iron man or hardcore mode, is a game feature that deletes the save file when the player dies, preventing any reloading to undo death. Diablo II's hardcore mode and the genre-defining Rogue popularized this mechanic. It developed from older suspend-save systems that were erased upon resuming play.
Savescumming is the practice of repeatedly loading saved games to undo unfavorable outcomes, making it impossible to permanently lose. It can be used to reverse lost battles, failed objectives, or bad luck in in-game gambling. Developers counter it with seeded random number generators and server-side save management.
A save state is a snapshot of an emulated game's random-access memory saved to disk, allowing players to preserve progress even in games that lack a built-in save feature. Nintendo's Virtual Console brought save states to mainstream use in the early 2010s. The Switch's Nintendo Classics calls them suspend points; Wii U and 3DS Virtual Console called them restore points.
Some designers use skeuomorphism to make save points fit the game world. Resident Evil uses typewriters that require ink ribbons, while Grand Theft Auto titles used cassette tapes, floppy disks, and compact discs to match their settings. In Chrono Cross, save points are story elements controlled by the antagonist FATE, and in Anonymous;Code the protagonist's save-and-load ability is the central game mechanic.