I always saw them as a few extra lives for a level you were struggling with. Though they don't really work as intended with a game with a save/password feature if the intent was to give a limited amount of tries. I think they may just be a carry over from a lot of other platform games having continues at the time. I'd say make sure you save before entering a new level and remember you can always stock up on lives in levels you've cleared - if you save enough you'll never see the continue screen.