What needs To burn fuel in rocket?

You need a fuel. You need something that will react or "burn" with it. This is called an oxidizer, even though oxygen is not always what is used. You need a means of forcing the fuel into a combustion chamber. You need a combustion chamber. And you need an exhaust bell for the spent fuel to leave! Some rockets need an igniter, something to set the fuel and oxidizer off. Other rockets use "hypergolic" fuels, which means that the fuel and oxidizer go off just by coming into contact. This is good because not having an igniter means one less thing that can go wrong. The lunar module had this kind of engine.

Solid rockets have the fuel and oxidizer mixed together, just waiting to be ignited. The burning fuel hollows the rocket out, forming a sort of combustion chamber.