Most, if not all modern FPS games released on consoles have adjustable sensitivity settings simply because it gives another dimension of control to the player. It's the same reason most operating systems include an option to change the speed of the mouse, or timeout for key-repeat, etc; different users prefer different input settings when they interact with their computers or consoles
Here's the general idea when it comes to video games:
A higher sensitivity on a console game (generally played with a gamepad) allows for faster movements, but is much more difficult, and takes more skill to play with precisely.
A lower sensitivity is much easier to perform precise movements with, but movement output is much slower, which is a disadvantage.
The 'default' setting in the game is usually the setting that the developers felt was the best balance of movement speed and ease of use for the majority of players, but the option is there for players who want to customize their input to a feel they're more comfortable with.