It's becoming more and more commong for games to have mandatory installs in order for them to function and run properly on consoles. Battlefield 4 on the Xbox 360 is such game.
The game will ask you for a mandatory 2GB install, which isn't that bad. However, if you want your game to run at an optimal rate, according to Digital Foundry, you'll need to install both the Single Player Campaign disc, which has an additional 5.8GB of data, and the Multiplayer disc which has an additional 6.6GB of data.
That means, depending on your dedication to both the single player and the multiplayer, that's a whopping 14GB install. As stated on the Battlefield 4 FAQ page, EA states "We highly recommend performing these additional installations to make sure you have the best experience possible in Battlefield 4."