Basically what I did was draw the images in Gimp (the background is just a blank piece of legal paper that I scanned), then use them as textures on rectangles in Blender. I then used the animation tools in Blender to move the rectangles around. I made images appear or disappear by sliding them in front of or behind the "paper" image. Setting the camera to Orthographic mode made it so when objects didn't change size as they moved towards and away from the camera.
Thematically, I think at first glance it may seem that the story in the animation is not at all connected with the ideas in the song. My modus operandi is to listen to a song over and over again, without ever trying to critically analyze it, and just see where my mind wanders. The story in the video came out of that process. I don't care to critically analyze either the video or the song, but I think if someone did, they'd actually see a lot of connections.