Halo 4 is the beginning of a new trilogy, but it does carry on from Halo 3... albeit 4 years later.
It's not necessary to play the earlier games, but it'll make more sense. If you're not planning on playing the earlier games (or don't mind spoilers) here's a very quick summary:
[video=youtube_share;NIwnrIOqhO8]http://youtu.be/NIwnrIOqhO8[/video]
Or, if you'd prefer something that isn't so cheeky:
http://en.wikipedia.org/wiki/Halo_(series)#Story_overview