Heat is the transfer of energy. Latent heat is the energy absorbed or released when a substance changes phase. So something taking energy from another thing is the same as the other thing "releasing heat."
Clouds form when water condenses into water droplets. That's a phase change, so the energy of latent heat is released into the surrounding environment, powering the storm.

Edit: I'm also not a meteorologist, and didn't give as detailed an explanation as grant.