Growing more and more antiquated, the continue finds its roots in coin-operated arcade games. A token usually gave the player a small number of lives depending on the type of game. When the player died for the last time, the game would pause and bring up the continue screen to ask whether he wanted to put in another token to continue playing. Most games used a countdown for dramatic effect or to return the game to its title screen in case the player had left.
In PC and console games, continues have become an arbitrary punishment for failure. If the player runs out of her allotted lives, a continue will replenish them, but often at the cost of bringing her further back in the game than she would have gone had she only lost a life. In games that use worlds and levels, often a life lost will return the player to the beginning of the level (or at the last checkpoint) whereas a continue will return her to the beginning of the world.
In games where the player has only one life, the continue screen tends to play the same role. Most games that do not award multiple lives often use a save game system; in this case, the continue screen also doubles as the menu where the player can load his last save.