Alphaville came out of the Berlin music scene of the early 1980's -- the members had been part of the Nelson Community, a short-lived art collective. The band consisted of keyboardists Bernhard Lloyd (real name: Bernhard Gößling) and Frank Mertens (Frank Sorgatz) along with singer Marian Gold (Hartwig Schierbaum).
The trio released the Forever Young album in 1984, and it would go on to be their biggest LP. In the U.S. , "Big in Japan" and "Forever Young" both charted, and hit #1 and #2 on the Dance Charts, respectively. While the Forever Young LP barely broke into the top 200 albums in the U.S. (peaking at #180), it became a top 20 album across much of western Europe.
The backstory for "Big in Japan" is interesting -- unlike the other songs on the album, it had been originally written by Marian Gold in 1979, and the title came from the name of Holly Johnson's band at the time. (Johnson would go on to form Frankie Goes to Hollywood.) Gold has stated the the lyrics were inspired by a story of a couple trying to get off heroin. The idea of going far away seemed to fit this story, so he used the phrase "Big in Japan" as the chorus.
As with many other groups, Alphaville was unable to keep it together, as singer Marian Gold left the band in early 1985. Alphaville continued on and had some modest success in Europe in the mid 1980's, while Gold's solo career never really gained any traction, leaving "Big in Japan" as their biggest hit.
Cool trivia fact: the video was directed by Dieter Meier of the band Yello.