Belting in general is loud, high and powerful singing, or well sometimes shouting.
Kire is in essence just a name, but usually refers to a specific type of voicebanks: Powerscale.
A Powerscale is a Voicebank that gets stronger with each pitch. The best example is Namine Ritsu Kire:
It starts at a weak A3 Pitch, goes to a natural D4 Pitch, leading into a strong G4 and ending in a belting C5 Pitch