In Slate, Bryan Curtis also wonders what the AFI "Cheers" list means: and
First, let's clarify what exactly Hollywood means by inspiration. To judge by the AFI list, we can define it three ways: Frank Capra, Steven Spielberg, and Tom Hanks.
[Most of the films on the list are] testaments to the indomitable human spirit. But apparently the AFI feels that there's more to movie inspiration than the heartwarming. For example, what's Stanley Kubrick's 2001: A Space Odyssey (No. 47) doing on the list? Its prescient vision and special effects might inspire awe, I guess. That might be the reason the AFI was inspired by Spielberg's Close Encounters of the Third Kind (No. 58), a movie in which a man abandons his wife and children to commune with aliens. In fact, the more you peruse the list, the more elastic AFI's definition becomes. Inspiring also means "rousing" (Gunga Din, No. 74), "religious" (The Ten Commandments, No. 79), or simply "well-acted" (The African Queen, No. 48).
Perhaps the most efficient delivery vehicle for inspiration is the sports movie: Hoosiers, Rudy, etc.
As for what these "inspiring" movies actually inspire? "It's just a hunch, but what I think inspiring movies do more than anything is inspire more inspirational movies."