An air pump and air stone/wand can help with the diffusion of gases (mainly oxygen / CO2) between the water and the air.
It's more valuable to have one in a tank that does not have a lot of "open air circulation" (a hang-on-back filter that causes a waterfall is "open air circulation") and does not have much in the way of live plants - because if the water is not sufficiently agitated, the O2 levels in the water can deplete and cause your fish to have trouble breathing.
If your fish seem to be doing fine and aren't gasping for air, an airstone is not particularly necessary.