The idea behind Stories is to allow you to string together multiple snaps to form... well, a story of course. And, unlike normal Snapchats, Stories will survive for a full 24 hours, so you can continue to add pictures to the story, and your friends can see the tale unfold as you progress through. The 24 hour clock is important because, as Snapchat says, "Your Story never ends and it’s always changing. The end of your Story today is the beginning of your Story tomorrow."
Stories will make it for an easy way to allow your friends to quickly catch up on what you've been doing for the past day. This is a major shift for Snapchat, because now instead of just being a messaging platform, it is moving into competition with services like Facebook, Instagram, Twitter, and Google+. But, the 24-hour time limit could be the make-or-break feature, because it will either lead to Snapchat being stickier (can't miss anything!) or Stories failing (it's not that important...)
The update for both iOS and Android is live right now if you want to give it a shot.