If you want to get into the nitty gritty details of how it works you can find the whole white paperhere. The TL;DR version, however, goes something like this:
The Speed Booster is what’s called a focal reducer (see diagram below), basically an inverted teleconverter. Where a teleconverter increases magnification, the Speed Booster has a magnification of x0.71. Because of this, more of the image and more light is able to fall onto the sensor
When you attach a full-frame lens to the adapter, it will give your mirrorless’ APS-C or MFT sensor nearly full-frame coverage out of that lens, while increasing the amount of light hitting the sensor by one stop. So a 50mm f/1.4 effectively becomes a 35mm f/1.0.
Because of the way the adapter works you’ll have to use full-frame lenses if you’re using a Sony NEX body. However, micro four thirds speed boosters are also in the works, and those sensors are small enough that you can attach EF-S or DX lenses to the other side.
The Speed Booster will cost you $600, and should be available starting sometime this month. The EF to E-Mount Speed Booster is already up for pre-order; however, speed boosters should releasing shortly for both Canon EF and Nikon FX lenses adapting to both E-Mount and Micro Four Thirds systems.
Thanks for sending in the tip, Troy!