Jesse Brightman is a neighborhood teenager who lives near Dexter and Rita's house. There is a vandal in Dexter's community, and he thinks it's Jesse. He has to deal with this vandal thing so he can come in and out without a Watch thinking it's suspicious (the Watch is set to get the vandal). Dexter enters Jesse's house, only to discover that the vandal is his father.
Astor also seems to have some kind of romantic interest in him, even though he is much older than her (in "Blinded By The Light" they are seen talking, and he tells her to which college he is going).
He, apparently, is a rebel because his mother died.