Chief Resident varies from specialty to specialty. SOme programs (particularly most of the surg subs) make all their senior residents chief residents. others make the chief year an extra year after residency (usually with an attending level hospital position). others select one or two senior residents to serve as chief.
i'm currently a chief resident in my program (along with another 3rd yr resident). i didn't compete -- i was appointed by faculty, my chair and my program director, so it's a position of prestige or "recognition". i am very involved in an administrative role within my residency. i don't make any extra money for it. we are the troubleshooters for all things that involve our residents. it's a busy job, but very rewarding.
it really shouldn't help anyone get into a fellowship, as most residents have committed to fellowships well before their last year of residency...but it doesn't hurt.