What does it do?
(I know how to activate it already)

I know it speeds things up, but how does it do that?

“Scratch loop blocks are programmed with a slight delay between repetitions and thus actions are performed slowly for new Scratchers to understand. If this delay did not exist, simple motion scripts could cause a sprite to fly off the screen instantly, confusing someone who was unfamiliar with programming. The repeat blocks (and forever), the wait blocks, the glide block, and the broadcast blocks have this delay. During this delay, an additional screen refresh is done: Scratch redraws the entire Stage. This is also a big source of lag.” (Scratch Wiki)

Turbo mode runs the project without the short delay and the screen refresh, I think.

I guess it also cheat speeding up the script timer somehow, cos I've seen weird behaviours in some script using the timer as delay in a loop.

I think the best way to think of it is that the script is no longer synchronised with the screen update which runs at 30 fps, because its not waiting for that sync the scripts run faster but because it is no longer synced then movement on screen can seem erratic.

I'm new to Scratch. Where is the “official documentation” for settings like “Turbo Mode”?

Don't think there is an official document especially for turbo mode. You can find information in the wiki though.