To form Al2O3 you need both Al and O2 (oxygen gas is a dimer):
Al + O2 -> Al2O3
But this equation is not balanced. To balance it, first equate the number of oxygen atoms:
Al + 3O2 -> 2Al2O3
Now you have 6 oxygens on each side, but the Al is not balanced so you must add Al on the left hand side.
4Al + 3O2 -> 2Al2O3
And its balanced!