Jesse Jackson is an African-American civil rights activist. He appeared in the episode "With Apologies to Jesse Jackson" where Randy Marsh "apologized" to him after saying the N-word on national TV, by literally kissing his ass.
Jackson also briefly appeared in "Trapper Keeper" to support the African American students in the kindergarten class during the class vote, however he immediately left after Mr. Garrison told him that there were no black students.
Jesse Jackson is African-American. He appears to be drawn with a strange eye shape, which are almost circular, as opposed to the elliptical eyes most characters are drawn with. He has black hair that is greying. In "With Apologies to Jesse Jackson", he is dressed in a grey suit and pants, a white shirt and a red tie.
Obviously, Jackson is extremely passionate about civil rights, doing whatever he can to ensure African-Americans are not discriminated against and sufficiently represented. However, he is also implied to be slightly egotistical. After Stan Marsh thought that the ass-kissing would make everything okay, Token Black declared that Jesse Jackson was "not the emperor of black people!" Apparently, however, Jesse Jackson had previously claimed he actually was.