quick and dirty answer
Basically stars are converting hydrogen into heavier elements (a process known as fusion), which released heat in the process. This heat attempts to make the star expand, which is held in check by the immense force of gravity.
A couple things to note:
1) It is gravity that is responsible for starting the fusion process. The stars accrete matter until they have a critical mass, at which point the gravitational force acting on the atoms causes them to undergo fusion.
2) As the star "burns" (it is not on fire, fire requires oxygen) it loses mass. This reduction in mass means that, over time, the gravitational force will not be enough to hold the star together. At that point we get a fireworks display known as a nova, or if the star is large enough, a supernova.