This song comes from a later period in their career, specifically from the album Achtung Baby. When AB came out, I was jarred at first. The band that had specialized in straight-ahead, earnest rock-and-roll was now experimenting with different rhythms and styles. "The Fly", the first single, was very Eurotrashy in its timbre, and it almost put me off buying the album. As I kept listening, however, I accepted U2's new direction and followed them through the following years.
This track, along with "One", is my favorite off of Achtung Baby. It was apparently first inspired by the film by German director Wim Wenders. Looking past the superficial association, it is open to interpretations; it could be a document of the last date of a dysfunctional couple, or a look at the Last Supper from the point of view of Judas Iscariot. Either way, it's a lush and romantic-feeling look at the end of the road (from an emotional viewpoint. Especially given the attention given to the prediction of the Rapture made for this past Saturday, I figured this was as good a time as any to post this.
U2 apparently never created an official video to "Until the End of the World", but here is a live performance from Slaine Castle, Ireland.