Cool Jazz really started to get popular in the US after World War II. It is a modern jazz style differentiated from Bebop due to the lighter tones and a relaxed tempo. In addition it differs from the Hard Bop style which followed due to the music using formal arrangements with elements of classical music versus a basis of blues, r&b and gospel that Hard Bop is known for.
When most people think of Cool Jazz, the one and only Miles Davis is the first artist that comes to mind. Some other great artists to check out include Chet Baker, Stan Getz, Dave Brubeck, John Coltrane and Gerry Mulligan.