Depends whether you are looking at a political map or a geographical map.
Geographically, The British Isles is an archipelago consisting of the islands of Great Britain, Ireland and many smaller surrounding islands.
Politically, the propper name for the UK is United Kingdom of Great Britain and Northern Ireland. It is the island of Great Britain the nothern part of Ireland (Nothern Ireland) and the nearby islands (but not the Isle of Man or the Channel Islands). Usually, it is shortened to United Kingdom, UK or Britain.
If you’re really interested Wikipedia has an entire page (quite a long one) trying to explain it all. http://en.wikipedia.org/wiki/British_Isles_(terminology)