My first instinct was that Mark Rosewater, the head of Magic R&D and the writer of the weekly column "Making Magic" on the official site, must have written a definitive account of the Magic colour pie. And with ~50 columns a year under his belt for the past decade or so, I'm sure he's written a million things on subject, especially as the colour pie is one of his favourite themes.
Finding a definitive "MaRo tells the colour pie like it is" article is difficult though, especially as the colour pie morphs and shifts over time, through Mark's best efforts and despite them. (I remember he spent quite a long time harping on about recent card Hornet Sting, as in his opinion it is an abomination to give green a direct damage spell of that sort.) However, I reckon if you read back through the Making Magic article archive, looking especially for pieces that are about defining the nature of the colours, you'll quickly start to understand how the people who make the game see their different roles, philosophies and abilities.
In the interests of providing a pat answer to your question though, check out this wiki article courtesy of excellent fan MtG site mtgsalvation. It's a pretty good attempt to define and collate all the things about each colour that make that colour what it is. And, oh look, it's got helpful links to some of the best Mark Rosewater articles on each colour at the bottom of the page. Sorted!
