A hurricane is a heat engine. Its fuel is the heat stored in warm ocean water, carried into the air as water vapour.

1. Warm seawater evaporates. Each kilogram of water that evaporates takes up energy from the ocean, the latent heat of vaporisation.
2. Moist air near the surface is drawn towards the low pressure at the centre and rises in the eyewall.
3. As it rises it cools, and the vapour condenses into cloud droplets. Condensation gives that latent heat back to the air.
4. The air is warmed by this release, so it is lighter and keeps rising. That helps to keep the pressure low at the surface, which pulls in more moist air. The loop feeds itself.

If you want to see how rising air cools and clouds form, see the Weather Island lab, "Lift air, make a cloud".