American Wire Guage works on the principle that smaller the number (generally), the thicker the wire. So 8AWG wire is thicker than 10AWG for example.

You can go too thin. I've had a wiring loom from one of my beetleweights catch fire due to a short. It was using 26AWG wire (which is the same guage of wire as that used on the RC wires to the receiver) and normally is OK in the low powered application I use it for in the BW (Shu! for the record) but when it faulted, I distincitly remember the smoke and then the wire glowing before it melted like a fuse would do. Left a nice burn mark on my hand that did.

Similarly with my Middleweight, when that developed a short during the middle of a battle with some Heavyweights, the RC wire melted. That would officially be the first time any of my robots have caught fire during a fight.

You can also go too thick where it'd be impractical to use, heavier and introduce uncesserary resistance in the circuit, it depends on the load being applied through them. The 12 or 14AWG wiring recommendation is from components I've used in the past where they've been that guage before.