How did athens benefit from victory in the persian wars?

Mainly from "tribute" -- taxes. The cities they took from the Persians paid annual tribute to Athens, greatly enriching the city. The Athenian Greeks also used the conquered areas as colonies, giving land grants to Greek citizens in the conquered areas, as there was little land left in Attica (where Athens is) that wasn't already owned.
The tribute was in the form of grain, precious metals, and work products (leather, pottery, etc.) which Athens usually traded (except for the grain) to further enrich the city