Green has a serious, calm, and focused personality in everything he does. Although Red and Green were once bothered by each other because their personalities are so opposite, they ended up resolving their differences. Green and his Strike were trained by Shijima of Tanba City when he was a child. Thus, Green has some cursory knowledge of martial arts, and his Strike knew Generation II techniques.

Spoiler

Green's special skill, as described by Dr. Yukinari Okido, is Pokémon training—that is, leveling them up and making them strong, and as such is referred to as the "Trainer".

(Source: Bulbapedia)