Along with Vector and Charmy, Espio played a minor role in season 2, only appearing in Episode 39 to help find Cream when Chaotix was hired by Vanilla, Cream's mother.
They play a larger role in Season 3, first appearing to bring Christopher Thorndyke supplies from his parents.
The second time Espio appears, he reluctantly helps Vector and Charmy help Tails get Cosmo, a girl he likes, to like him back, and after that appears with the others to help fight the Metarex.
Espio states in his first appearance that he's the brains behind the Chaotix (to which Charmy claims that he's "Super Full of Himself"), when in the Sonic Heroes instruction manual, Vector is stated to be the brains.
In the anime, he's sometimes seen as a comic relief character as he has been hit (unintentionally) by Amy's hammer, woken up by Vector when he had pepper poured on him and was discovered in a humiliating way shortly before being beaten up.
Espio is the quietest, most sensible of the three and regularly goes head-to-head with Vector over his crazy schemes.