It's a buddy movie set in the early 60ies Jim Crow South, working class Italian Brooklyn bouncer - Tony Lip (he of Sopranos fame) played by Viggo Mortensen - drives ultra-refined black (and gay) classical-turned-jazz-to-earn-a-living pianist - Don Shirley played by Mahershala Ali - on a tour through the South. Tony is a unabashedly racist initially, but has a heart; Don doesn't quite know where he belongs ("If I'm not black enough, not white enough, not man enough, then what am I, Tony?!" is his key outcry in the movie), but sees himself pushed again and again into the "negro"-bracket by people and times. The "Green Book" was a lodging and accommodations guide for black motorists travelling the South - places where they would not be turned away or beat up.
Ali won an Oscar for his supporting role as did the movie as such and the original script.
The film received some criticism from the Shirley family (doubting that Don was ever friends with Tony and the latter not just his employee) and from people bemoaning that it was yet another "white savior"-story. (These days you can't even make a film AGAINST racism anymore without rubbing someone in the wrong pc-way.) I didn't see it that way, if anyone was saved in that movie then it was Tony Lip who had his horizons broadened from his initial ignorant racism. (Back in the early 60ies it was easier to get someone rid of his individual racism than free yourself as a black man from the implications of the general racism all around you.)
Green Book isn't an agitprop movie (it plays in the months before Christmas and you can guess where Don Shirley will somewhat unsurprisingly end up on Christmas Eve and how a bunch of Brooklyn wops overcome their resentments when it comes to sharing food). It's quiet, told straightforward very conservatively and there are no surprising twists, but I liked it. The music - Don Shirley's idiosyncratic mix of jazz, easy listening, classical runs and gospel lovingly recreated and rerecorded by Kris Bowers - struck a chord with me.