The Daily Dot:

To shoot the video, the band hopped aboard a special fixed-wing airplane, lovingly dubbed the “vomit comet” by astronauts in training thanks to its ability to induce, well, vomiting. The plane, provided and operated by the company S7, climbs higher than a commercial jet and then the pilot begins to take it on a parabolic flight pattern. In other words, the plane goes up at a steep angle, then back down again, creating 25 seconds of weightlessness for the cargo (i.e. OK Go and crew).

Dave posted this morning about the video. Here are some details about how they accomplished it.