"The Lobster" is, according to Wikipedia, an "absurdist dystopian comedy-drama." This seems fairly accurate. It's directed by Yorgos Lanthimos, known for Greek language absurdist films.
Colin Farrell plays David (he may be the only person who ever gets a name in the movie) whose wife has left him. So he's escorted to "The Hotel," where he has 45 days to find a partner or be turned into the animal of his choice. He's asked to make that choice very early on in the film, and he chooses the lobster.
I should acknowledge that I'm not generally a fan of absurdist movies, but if they're well done they can still win me over. But the biggest failing of this movie was taking people and reducing them to a "defining characteristic" (a term used more than once within the movie - a limp, nose bleeds, a good singing voice, near-sightedness) that's the only thing that defines them and the only commonality they have with their partner. Humans are complex, and it's what makes us interesting. Turning us into walking "defining characteristics" makes the people in the movie one dimensional, unappealing, and uninteresting. He's using this to comment on human relations and interactions, but if the people don't feel real, it weakens the story. The movie as a whole is somewhat interesting - as in "where the hell is he taking this horror show?" - but certainly not a favourite of mine.