An analogy: If you’re playing chess and need to pack the game away, you can write down a list of where every piece is and whose turn it is, then put the game away and re-set it up later. That paper is your saved game.
Video games do a version of this. They take the current state of the game, simplify it down to the details that they need to reconstruct the current state and save those details on your hard drive.
(There’s usually a lot of details for some games, for others it’s literally just a “the player is at this chapter”. There’s compression and a lot of other stuff going on as well.)
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