It doesn't have to read so much and spin the game as much that way. Less risk of general wear and tear from a lot of play.
It also is less intensive on the reading, and it is possible that if your disc got scratched real bad that if it was installed the game would still work. I know some folks who got real deep scratches, borrowed the game from a friend and installed it and got it working without needing a replacement.
Also can cut down on load times if a game has heavy load times. Reading from hard drive is definitely faster than reading from a disc.
Faster loading. MY THEORY: And if the disc is scratched so bad that you can't even play it but if it is installed, if the Xbox 360 is still able to read the game, you should be able to play it perfectly no matter how bad the disc is scratched but as long as the Xbox 360 can recognize the game. --- I am the Thunder Dragon! Xbox 360 Gamertag: TDPNeji