According to the question, a battery was used to light the steel wool by bringing the terminals very close together. When the battery came into contact with the steel wool, current was sent out through the thin wire. This caused the iron to heat up quite well.
Iron reacts with oxygen under these conditions as follows;
2Fe(s) + 3O2(g) --------> 2FeO3(s)
This is the chemical reaction that occurs when the steel wool is set on fire.
