The idea behind a metal air battery is to use air—which is free, lightweight, and widely available—for the cathode part of the battery. Metal air batteries basically suck in the freely-available air and can ditch the heavy casing that would normally hold the anode material inside the battery. Using air basically makes these batteries fundamentally lighter and cheaper.
Fluidic Energy makes a specific type of metal air battery called a zinc-air battery. Zinc, which is abundant and low cost, is the key material that sits in the electrolyte of their battery and moves onto the anode during charging and discharging.