2005 BMW Ci Fake Stick Shift

[TheSixthSin]

This seems like a good place to ask this:

I have a 2005 BMW Ci, sports package. I don't know much about the technical parts of a car, but there's a shift mode at the very back (front: Park, Reverse, Neutral, Drive, and a "-M/S+"). What does it do? I heard that it was called stick-tron or something like that; it's not a real, traditional stick shift because there's no clutch, all I have to do is pull the lever back and it'll go to that mode. But I can also move it side to side, forward and backward. What do these modes mean? Whenever I move into that M/S mode, moving up causes my dashboard to say M1; moving it side to side and back will make it read M2, M3, S, and I think that's all.

When is it suitable to go into each mode? I tried going to M3 today and it felt like I was in a rocket, with a roaring engine. I want to be able to use this function but the BMW manual didn't say much about this and neither did anything I looked up online.