Thanos is preoccupied at the start of the film, so sends the Black Order to Earth to try to get the Infinity Stones for him.
Proxima Midnight and Corvus Glaive go to Edinburgh, to get the Mind Stone off Vision. Vision and Scarlet Witch are rescued last-minute by Captain America, Black Widow and Falcon.
The big round thing hovering over NYC is Cull Obsidian and Ebony Maw's ship. ("You can't park here, buddy. Earth is closed today. Take your tractor beam and skedaddle." - Stark)
They've come to get the Time Stone off Doctor Strange. Stark tries desperately to get Banner to hulk out, but he can't. ("Don't embarrass me in front of the wizard" - Stark)
Thanos is "the main character" of the movie.
Infinity War won't be especially funny (in comparison to Homecoming and Ragnarok). "The one thing that character deaths do is remind you that the world has real stakes. Death is a real possibility in the storytelling" - Anthony Russo.
Joe Russo says "you should go back and look at clues in Civil War to what's in Avengers 4." Anthony Russo says "it's more of an epic adventure in the classic sense, with huge emotional stakes."