Aluminium reacts with iron(III) oxide because it can be considered to be more reactive than iron so will remove oxygen from the iron(III) oxide.
Aluminium reacts with iron(III) oxide in a very spectacular fashion releasing a lot of heat. It is termed the thermit reaction for which the equation is:
In terms of electrons:
When you talk about stability you must ask yourself stable with respect to what? If you leave a piece of iron lying around exposed to the environment it naturally reverts to iron(III) oxide or rust which is brought about by the action of air and water. So in fact you can consider iron(III) oxide to more stable than iron i.e lower in energy.
It is quite difficult to turn the iron(III) oxide back to iron. In this reaction a more reactive metal such as aluminium is able to reduce the iron(III) oxide back to iron.
Even then it is hard to get the reaction to go as the activation energy is very high so a fuse of burning magnesium is used.
The result is spectacular.
(From BBC tv)