Background
She is the daughter of Ellen Harvelle and Bill Harvelle.
Season 2
Thinking Dean is an intruder at the Roadhouse, Jo holds him at gun point. He disarms her, but she punches him in the face.
While Dean notes that "normally I'd be hitting on you so fast it'd make your head spin", in the wake of his father's death and the secret he is carrying, he concludes it is "wrong place, wrong time."
Jo wants to go off hunting on her own, but Ellen doesn't want her to. The reason Jo wants to be a hunter is to feel close to her father, Bill Harvelle, who was a hunter that died while hunting with John Winchester.
Even though Ellen gives the case she has researched to Sam and Dean, Jo sneaks off and joins them, getting Ash to help her cover her tracks. While working with the Winchester brothers, Jo is kidnapped by the spirit of Dr. H.H. Holmes. Dean and Sam are able to rescue her. She then helps capture and trap Holmes, although a disapproving Ellen appears to bring Jo back home.
Ellen reveals to Jo that her father was killed while hunting with John Winchester and Jo confronts Dean and Sam with this knowledge, apparently blaming John, and by proxy, them, for Bill's death.
In Hunted it is revealed that Jo had left the Roadhouse to become a hunter, against Ellen's wishes, although Jo is still sending her postcards.
She is working in a bar in Duluth when Sam, possessed by Meg arrives. He teases her about having a crush on Dean and then takes her hostage. The demon taunts her about her father's death. She relates what Ellen told her, in which John exposed them, leading to Bill's accidental death. However, the demon claims that Bill barely managed to survive the attack; "Bill was all clawed up. Holding his insides in his hands. He was gurgling and praying to see you and Ellen one more time." The demon then claims that John shot him to end his suffering.
After Dean arrives, Evil Sam turns his attention on him. Dean reveals that Sam is possessed and frees Jo before going after Evil Sam. Using the ringtone of his cell phone, Jo finds Dean half-drowned after Evil Sam has shot him. She bandages his wound and expresses a desire to come with him in pursuit of Evil Sam, but Dean refuses. Dean promises to call, but Jo whispers, "No, you won't." That marks Jo's final appearance on Supernatural until Season 5.
The accountability of the demon's claims is doubtful, as the Meg Demon wanted to make Sam appear evil in order to make Dean shoot him. The demon could have lied, as demons have been well known to do, although when Jo asks, Dean mentions that they occasionally tell the truth "if they know it'll mess with your head." It is therefore open to speculation whether or not John shooting Bill to "put him out of his misery" is the true version of events, or if the demon was merely antagonizing Jo to further the rift between her and the brothers.
Season 5
In Good God, Y'all, Jo and her mother, Ellen, end up in a small town called River Pass in Colorado. They were there to help Rufus, a demon hunter and one of Bobby's friends, to help kill the demons that have laid siege to the town, but both mother and daughter were separated in the chaos. Later Jo finds and joins up with Rufus and some other townspeople. Eventually they attacked Sam and Ellen, both of them appearing to be possessed by demons. Jo joins in with Rufus to torture the supposed "demon" out of a captured Sam with holy water and salt, but ends up doubtful when no effects on him are present. Dean and Ellen arrives and after a brief struggle, both manage to convince Jo and Rufus that War, one of the four horsemen of the Apocalypse, was responsible for making all the people in town turn against each other by thinking that both sides are demons.
In Abandon All Hope..., Jo and Ellen decide to help Sam, Dean, and Castiel kill Lucifer. They split into two groups being Sam and Dean, and Jo, Ellen, and Castiel. Castiel is eventually trapped in Holy Fire by Lucifer.The group continues into the town and is confronted by Meg and several Hellhounds. They escape into a store, but not before Jo gets mauled by a Hellhound. With desperation, Sam and Dean make a bomb and Ellen decides to stay with Jo, saying someone needs to open the door. Jo and Dean share their first and last kiss before the Brothers leave. Eventually, Jo dies in her mother's arms and Ellen is left to blow up the building.