There is very little speaking throughout the movie. Only one scene features much talking and it's not even a conversation. One man launches into a lengthy, detailed monologue about the infinite size of the universe and our relative insignificance within it. The man believes that the speech is profound and laudable, but in reality it sounds like something a college kid would say while high at a party.
The gist of the man's speech expresses that the universe is too vast for any of us to truly leave a legacy when we die. The ghost (played by Casey Affleck) is especially compelled by this speech because he has just died and is now especially compelled by things concerning his legacy.
The ghost observes what he cared about most while he was alive. He haunts his house. He observes his wife, struggling to watch her struggle to cope with his death. He wants desperately to comfort her, but cannot. It's heartbreaking.
In addition to heartbreak, this movie evokes many other feelings: warmth, humor, boredom. Boredom comes up a lot. For every genuinely beautiful and moving moment of the movie, there is at least five minutes of emptiness. The runtime is short, just over 90 minutes, but it feels longer and could easily have been trimmed by 20 minutes.
One scene in particular that involves a pie seems to drag on for at least four days, even though it actually only lasts four minutes. In the moment, the scene is likely unbearable to many viewers. I plead for your patience. Do your best to empathize. Think about how you would feel in the situation. Do this, and the scene becomes haunting and powerful.
That's probably the best way to sum up the movie—many scenes may feel boring if given little thought, but are actually deeply moving if given honest consideration. Not all scenes fit this description—some, no matter how much your squint, are just extended moments of vapid emptiness. The emptiness outnumbers the deeply moving by about 2:1, so this movie requires patience and commitment. The movie contains no conflict, only contemplation and some glorious music.
If that sounds like enough for you, give this movie a chance. But fair warning: if you bore easily this movie will feel like a waste of your time.