The term "organic battery" is used to describe a living creature being used by a machine as a power source, whether it be through siphoning off the creature's body heat or the body's own chemicals, etc.
In Sonic the Comic, organic batteries are Mobians who have been sealed inside Dr. Robotnik's Badnik robots. The science behind it is never fully explained, but it is likely that the Badniks use the bioelectric energy and/or thermal energy generated by the living people inside their chassis as fuel. Since living creatures need to eat and sleep to build and conserve energy, Badniks would likely need to as well. A possible example of this has been displayed in Sonic the Comic #75 in the Tails story, Fox On The Run Part 3. Tails and Tantrum are captured by two Badniks who intend to eat them, but Tails and Tantrum escape, leaving the Badniks to resort to eating fungus and cavern mould.
However, Badniks are often seen working perfectly well without an organic battery and many Badniks spend their time attempting to capture Mobians in order to actually gain a battery. Day of the Badniks sees Stripes and Ruff get captured by two Badniks and become organic batteries, although they have a slight consciousness moments before they are converted. A badger in Megatox comments that he thought he was going to spent the rest of life inside a Grabber for not working hard enough.