Tetris Evolution (Xbox360): WTF is a T-Spin?

I've played a lot of Tetris in my life. I never heard of a T-spin, but it sounded perverted! The manual doesn't explain it and the in-game help isn't much better. Instead, it's a technique with the T-shaped piece:

2. 
   Have a T-shaped piece in storage to make this easier.
   
4. 
   Create a T-shaped hole with one block overhanging block on the row above (Left part of diagram).
   
6. 
   Let the T-shape land sideways. You'll hear a click (Middle part of diagram).
   
8. 
   Rotate the block once so that it fills the T-shaped hole. (Right part of diagram)
   

Do this procedure, and you'll get the "Rollin On Spinnas" Achievement.

Do this procedure where the T-shaped hole completes 2 rows simultaneously, and you'll also get the "T-Spin Deluxe" Achievement.