the fellowship is the governing body of the college, normally made up of some of the college tutors and people like the bursar. All souls is special in that it doesn't take any students, and all its members are fellows. Every year they award prize fellowships to the university's top finalists, through a process of exams, interviews, and dinners- those sucessful get a ten year appointment to the fellowship with stipend and accomodation provided if they want it to do whatever they want- most do D.Phils then become academics, but there's no restriction.
At a minimum, it's probably the most prestigious academic award an undergraduate can be given. Beyond that, it solves all your funding problems for pg. study and puts you in a very good position for getting academic positions after your tenure if you wanna follow that route.