"Subsequent playthroughs" means playing a game or going through an experience again after you have already played or experienced it before. Full definition
Achievement Unlocked: Attempt to find secrets and complete difficult challenges on subsequent playthroughs. (onrpg.com)
It's a clever platformer that embraces the frequent deaths that are a hallmark of the genre by forcing you to use your own corpses in subsequent playthroughs in order to pass its levels. (toucharcade.com)
I like that when I unlock achievements in Mass Effect that it affects how I build characters for subsequent playthroughs. (snackbar-games.com)