Jesse is the Fitzgerald's oldest, and most invisible, child. Kate has leukemia, Anna "gets" to donate blood and plasma and marrow, and Jesse… well, Jesse burns things down for attention. He tells us, "I am the kid who played with matches" (3.1.1), and we see him burn down abandoned sheds, warehouses, and schools. (Is there a fire in the disco? Fire in the Taco Bell?)
He feels helpless, not being a match to donate an organ to Kate, which might be the only thing that could get his parents attention. (Pulling off his own braces with a fork before he became an arsonist sure didn't work.) He is kind of on Anna's side, too, since he's the one who takes her to visit Campbell in the first place.
Jesse doesn't seem to have any friends either, other than Duracell Dan, the homeless dude who watches over Jesse's firebug stuff in exchange for a Value Meal a few times a week. Jesse's fires get larger and more reckless as he gets more and more desperate for attention, almost as though he wants to get caught. He almost kills a bum (whom he rescues, because he's not trying to kill people), and he steals a judge's car.
Eventually, his dad finds out (because Jesse leaves all his fire making equipment lying out in the open) and hugs him and… that cures everything. Hugs, not firebugs, people. We find out in the epilogue that Jesse graduates from police academy. Either he's going to be in a new movie, or he's gotten his life back on track.