Bill Cosby: Himself was easily one of my five most watched movies as a kid, right up there with Return of the Jedi and Raiders of the Lost Ark. We had a VHS copy that we had recorded off of HBO, with a printed sticker on the front with the hand-written title, and we would put that thing in and watch it what seemed like once a month.
In the late 70s and early 80s, Bill Cosby was already an established comedian whose laid back and casual demeanor was what set him apart in his story telling ways. He was a family-friendly performer, and a 'traditional values' family man to boot. His style was easily more accessible to the common fan of comedy, and a welcome apart to the more edgy, dirty (and arguably popular at the time) routines of Richard Pryor and Eddie Murphy. Essentially, his Cliff Huxtable from The Cosby Show is a pretty direct reflection on who he is as a real-life person.
What set Bill Cosby: Himself apart from his other earlier routines (the Fat Albert bits, his stories as a kid in the streets) was that he was a little more animated than usual, at times. The majority of the movie is set with him sitting in a chair, speaking to the audience as would a grandfather to his young grandchildren, telling stories in a manner that is his typical casual, but then with the mannerisms of a physical comedian.
Throughout its run time, Cosby speaks maybe two minor curse words, showing that comedy doesn't necessarily have to be littered with f-bombs or the damning of God. The following is such a bit, that perfectly portrays why he was one of the most popular names in comedy and family television in the 1980s (if you haven't seen the entire movie, you will do yourself a great service and see it on Netflix or even Youtube):