Up until maybe the late '80's, they were made in Japan. They were made for Western States Importers (WSI) in the U.S. I think production moved from Japan to Taiwan in the late '80's. There's a connection with the Diamondback brand, although I'm a little fuzzy on exactly what it is (others will know). In my opinion, they're typical of Japanese-built bikes from the late '70's to the '80's: excellent value, generally good build quality, etc. Like most brands, Centurion offered bikes that were entry level, and they made bikes that were race worthy, and everything in between. It just depends on the model. I've got two Centurions, one an entry level road bike, an '85 Accordo, and the other a top-of-the-line touring bike, an '83 Pro Tour. For what each of them are, they're both very nice bikes in my opinion.
BF member T-Mar is an expert on Centurions.
Here's an article about Centurions on Sheldon's site:
http://sheldonbrown.com/centurion/index.html
And here's another link to Sheldon's site, the '84 Centurion catalog, to give you an idea of the range of bikes they offered:
http://sheldonbrown.com/centurion1984/index.html