It's billed at IMDB as "Comedy , Drama , History". But prospective viewer be warned: it's very dark humor. And as that Stalin t-shirt proclaims: dark humor is like food; not everyone gets it.
But I pretty much got it, I think. It is a based-on-fact movie about the events in 1953, beginning shortly before the Boss's demise, continuing until shortly after his funeral, and the inevitable power struggle is resolved. It is a only slightly sped-up good-parts version of actual events.
It is a satirical picture of a society powered largely by terror. Violence is rarely pictured directly; the movie's R rating is based mostly on its language. If people running afoul of Stalin are lucky, it's off to the Gulag; otherwise it's a bullet in the head. No less fearful are those ostensibly in power directly underneath the Beloved Leader and Teacher of Progressive Mankind. But neither are they bound by any silly rules; when it's clear that there will need to be a new ruler, the competition quickly becomes feral, as former "comrades" realize it's betray-or-be-betrayed.
You ask: how can that be funny? It's hard to explain. Certainly because of all the absurdity involved, and knowing that we're watching this from our comfy couches, and not as a participant or victim.
Acting is first-rate. According to IMDB's trivia page, the director decided to not even try for Russian accents. So Steve Buscemi as Nikita Khrushchev sounds… just like Steve Buscemi.
And Michael Palin plays Molotov as the totally craven toady that he was; a Monty Python parody without mercy.