The first time you open the app, it'll pull together a library of all the Live Photos you have on your phone (so even if you don't have a 6s, but have been sent Live Photos from people who do, they'll show up). As you scroll through, you'll notice the app has automatically turned them into GIFs, and smoothed 'em out by running them individually through special video stabilization software. Suddenly, that Live Photo you took while jogging looks like it was shot on a Steadicam. If you want to see just how much smoother they are, tap on any and hit the semicircle icon in the bottom-left corner to remove the corrective stabilization effect.
If you want to show one off, tap the share button and share the GIF via text/email/Twitter/carrier pigeon -- finally making it easy to show off the full effect of your Live Photos with iOS-less pals.