It's a valve that sits in the hydraulic line for the clutch. It's supposed to let the fluid flow freely when you press the clutch pedal but slow down the fluid flow back and as a result of that slow down the speed with which the clutch assembly grabs the clutch plate. All this is done to avoid sudden loading of the driveling and potentially avoid broken gear teeth etc.
Now part II of the story is that even though it's supposed to have no resistance to the flow of fluid while pressing the clutch pedal it in fact does, very little and therefore the transmission stays "loaded" for a split millisecond longer.
So all and all it slows down the process of shifting.
On my coupe it's virtually unnoticeable and I didn't even bother removing it, on my wifes E90 328 however I can feel it more... sort of like on my E46.