Quicksave (according to Wikipedia, and my own experience) is a feature that allows the player to save their game state with a single keystroke, instead of (say) going through a lot of complicated menus. The "FPS" shooter Wolfenstein 3D (1992) had this feature.
I grew up with old 8-bit machines, where you could buy add-on hardware like disk interfaces that might have a special "snapshot button" -- but that doesn't count. It wasn't built into the game, and that matters because add-ons can add anything.
Were there earlier games with a built-in quicksave feature? What was the first game to have this feature?