Q: Why does your BMW need a performance rear differential:
Short Answer:
Improved acceleration, traction, and stability potential; as why all M-Series are so equipped.

Long answer in simple terms:
Standard open-type differentials, equipped in most non-M Series only send power to one wheel at a time in all conditions.
A Limited Slip Differential is able to effectively split power between both wheels at crucial moments (Note: This is by different means in different brands. LSD Vs TBD... OEM, Kaaz, Quaife, Tractive, Wavetrac ect).
When you launch your car from a stop, having the power continuously sent to both wheels increases traction exponentially. You leave the line with more power getting to the ground, and less power spinning your wheels; this is dramatically faster.
When your vehicle is turning, the outside wheel is rotating faster than the inside wheel; the inside tire is doing less work. The vehicle wants to 'lean' on the outside tire more further increasing it's load. While the outside wheel is forced to do more work the inside has less traction and therefore, in an open differential, the power wants to go to the wheel with the least amount of resistance and its wasted spinning the inside wheel when cornering hard.
Through various means, a LSD or TBD effectively splits power to both wheels and can aid in powering the car forward coming out of turns as both wheels are utilized most effectively.
When entering a corner, this balance of traction helps to increase the stability of the car when coming in at high speed improving confidence and safety. This leads to faster corner entrance potential.

Choosing to also equip shorter gears means that your effective acceleration is improved, at a varying compromise in top speed.