They form in water in the Intertropical Convergence Zone. Forming off the coast of Africa, for example, they move westward and eventually upward, pulled by the winds. Warm moist air is pulled into the center of the hurricane, where it rises. As it cools and condenses to form rain, it actually heats due to the energy required to cause condensation. This keeps it warm and accentuates the low pressure zone.
More air is drawn into the system, and it grows on itself.
This is a positive feedback system. Finally, the hurricane reaches land, where it is cooler and there is no moisture source, so it cools and dies.