Aeration causes agitation on the surface of the water. The aggitation and bubbles increase the surface area of the water surface and increase gas exchange - more oxygen in and more carbon dioxide out. The rising bubbles bring water up to the surface with them, helping tank circulation. All these functions can be accomplished without airstones, by using power heads or power filters. Bubbles rising in the tank can look good, and also be used to hide things that don't look good, like your power filter intake tubes, heaters. Just don't have the bubbles being sucked into your filter. I don't use them, I hate the darn pump noise!
And isn't it amazing how often other people have posted the exact same answers right ahead of you in the time it took you to type it? I must learn to type faster!