A battery is essentially an entire electron manufacturing process. It consists of two electrodes, the anode (negative) and cathode (positive). Usually these are two dissimilar metals such as copper and zinc. These are immersed in a solution (sometimes an acid solution).

A chemical reaction takes place at the anode that produces electrons. These flow through the external circuit to the cathode, where another chemical reaction uses up the electrons. The circuit must be completed inside the battery - this is often accomplished by having positive ions flow from the anode to the cathode.

A battery manufactures electrons at one electrode and recycles them at the other, but the electrodes are used up in the process and waste products are produced. This is why batteries run out after a while. In a rechargable battery the chemical reactions are run in reverse to repair the electrodes, but that can only be done so many times.

Fuel cells are essentially batteries where the raw materials are continually being added to the system, and waste products are constantly removed. These have the potential (pardon the pun) to be very useful sources of energy-on-demand in the future.