The M7 coprocessor in the iPhone 5S is a fancy name for a chip that counts your steps and motion all day, every day. In order to see how many steps you've been taking, you'll need to use an app specifically built for the iPhone 5S and the M7 chip.
While we wait for more developers to integrate the M7 and the stats it keeps into apps, there are currently five apps available that have already integrated with the motion tracker. Here they are in no particular order.
Strava Run This free app has been around for a while giving runners stats and GPS-created maps of running routes. With the M7 having the capability to discern if someone is walking or running (among other things), it only makes sense for the app to integrate with the new technology.
You won't find your daily step counts in Strava Run; instead you will find that it uses the M7 chip to automatically pause your current activity when you stop running, and provide better accuracy about your run.