Every life represents an Alternate Universe.Every time you die, that universe lost its hero. It's only the last hero, the one who beat the final boss and got the final credits, who succeeded in his own Alternate Timeline. Tens or hundreds of other universes The Bad Guy Wins. Villains such as Bowser, Dr. Wily, and especially Red Falcon won in more universes than they lost.
They are only illusionsIn fact, all the time you fought you were trying again, you were just looking at the Game Over screen, then whatever follows, in correspondence to your controls, but lives make you think you are continuing to play on. This illusion was created so players would have a sporting chance.
Extra lives, continues, and restoring saved games are just abandoning that Alternate Universe.Ala Higurashi no Naku Koro ni. Every time a character dies, they really do. Mario, Sonic the Hedgehog, the Hero from Dragon Quest. They really die. The Bad Guy Wins. The hero's soul and memories are moved to another dimension and rewrite their counterparts there who did not die, where they try again; but if they die again, that's another universe that falls to evil. Thus, evil wins in every dimension except for the last one.
Alternatively, all video game characters are capable of regenerating at will.