He is described by Luke as a no-good loser, who abandoned his wife and kid. Jess then leaves at the end of Season 3 to live with Jimmy in Venice Beach CA. Jimmy is the father of Jess Mariano.
Jimmy doesn't listen and goes to see Jess anyway and when Jess finds out Jimmy is his father it is a big shock. Jimmy tries to tell Jess he can't stay with him and his roommate Sasha but in the end he lets Jess stay. Jimmy seems insecure, kinda rattled with a frenzic energy, but also with the best intentions at this point in his life.
The following year Jimmy mysteriously shows up in Stars Hallow and when Luke finds out he tells him to stay away from Jess. Take your favorite fandoms with you and never miss a beat. That night Jess and Luke get into a fight that ends with Luke throwing Jess out.
Jimmy is first introduced when Jess's mother calls Luke to ask him to take care of Jess.
His family life in California with Sasha and her daughter seems fairly stable and he also owns his own business at Venice Beach.