Michael Keaton plays Riggan Thomson, an aging Hollywood actor who's mainly known for playing the action hero Birdman in a series of three blockbuster movies years ago. He's now trying to bring a play of Raymond Carver's short story "What We Talk About When We Talk About Love" to Broadway, but it isn't going well. He's having problems with his actors, and the voice of Birdman mocks him for his inadequacies.
The movie is filmed as if the entire thing is a single take, following actors through the halls of the theatre, onto the stage, up on the roof, out on the street to the bar next door. If you look for it, there are places where they must have made cuts (a passage through a pitch black corridor, or a few moments of a still scene), but even these are few and far between. It's impressive, unusual, and occasionally disorienting. It's also not clear how much of it actually happens, with Thomson performing telekinesis on several occasions, and an ambiguous ending.
I was impressed by it without actually liking it: there are a number of very good performances, and the visual style is nothing you've ever seen before. If you're a fan of movies, this is definitely worth seeing for what it says about actors, the acting, and for the spectacular filming.