Mike needs an external battery so he can charge his Samsung Galaxy SIII. Leo uses the 5600 mAh Anker Astro, and he can get two charges out of it before it needs recharging. It's also small enough to fit in his pocket.
There are a couple of things to pay attention to when purchasing an external battery. One is the capacity, which is measured in Miliamp hours. This should at least be equal to the Miliamp hours of the phone's battery with a little overhead. The other thing is amperage. The more amps, the faster the charge. If he can find one with 2.1 amps, that would be ideal.