Amber is the world created by Roger Zelazny. It is much like the garden of Eden; all the worlds are modelled after it, yet each is a flawed copy, or a Shadow, of the original. Like Eden was considered paradise, the ultimate in all Creation, so is Amber. This world is governed by a royal family, the Amberites (citizens living in Amber that are not of royal descent are amberites; note the difference in capitalization). Members of this family are able to wield incredible powers to twist reality, except for that of Amber, into whatever they desire. Amberites can travel through the shadows of other worlds using only the power of their minds, or the Pattern.
The Pattern is a central theme in the books. It is the source of the Amberite's power; only Amberites can walk the Pattern, and only they can wield the power from the Pattern.
Almost an antithesis of the Pattern, yet very similar, is the Chaosian Logrus. The Chaos realms are and are not like Amber. Inhabitants have strong powers, able to shapechange and travel across Shadows like Amberites, but they cannot walk the Pattern. The reverse is true about Amberites; without Chaosian blood flowing through their veins (and I mean through family ties) no Amberite can walk the Logrus.
Amber is a super complex world, and the above information doesn't even begin to do it justice. For a very quick overview check out the Amber RPG FAQ. When I first began this RPG I had not heard of the books at all, and this guide helped me play. Also, what follow are several links to Amber websites one may look through to find out any more information (and there is a LOT out there).
R. Zelazney's Amber Dictionary
The Hall of Mirrors
All Roads Lead... This page is an excellent source of web pages about Amber: Recommended reading
Another Amber FAQ
Amber Timeline Contains spoilers for the books; probably shouldn't read unless you've read the books
Roger Zelazny Page A page dedicated to the creator of the Amber series