Incipio calls its offGrid Pro a "removable battery case." All cases are removable, of course, but removable here is a reference to the battery inside the case which is indeed removable. In fact, you get two thin removable batteries, so if you need even more juice, you can carry that extra battery around and swap it in when you need to. One battery will charge the iPhone 100 percent (doubling the iPhone's battery life), so this battery case is rated to triple the battery life of your phone when you count that second removable battery.
You can charge your phone and battery in the case with a micro USB cable or use the separate battery charger, which can charge both removable batteries at once. Like other battery cases for the 5/5S, you may have some trouble accessing the headphone port on your phone, particularly if your headphone jack is superslim. Incipio, like Mophie, provides a short headphone dongle that works with any headphone jack.