Turbofan wheel covers have one purpose: to move air across hot brake rotors to cool them off. That and to look awesome. They were very popular in the 80s and 90s, especially on German makes – BMW, Audi, and Porsche. They saw a fair amount of professional racing use including Formula 1. As such there were hordes of aftermarket fan designs from European and Japanese wheel-makers.
Turbofan wheels were engineered to draw hot air from the wheel-well and out through the wheel itself, these fans saw widespread usage until modern brake technology and getting banned by various sanctioning bodies (some teams used them to evacuate air from under the entire car and were thus considered illegal active-aero devices) relegated them to the old-tech bin.
Old-style fan covers are definitely a love it or hate it style, so automakers eventually learned to integrate the air-moving power of the fan into much more standard looking wheel designs. Porsche Turbo ‘Twists’, C4 Corvette ‘Turbines’, and BMW’s new ‘Turbine’ wheels on the 2012+ 3-series ‘Design Line’ all being more modern examples. That said, a modern day revival of the turbofan wheel seems to be taking place and I love it.
A recent example of true turbofan wheels in use are the wheels on the Audi A1 Clubsport Concept car.
Ken Block even debuted some Turbofan wheels in Gymkhana Six:
Gallery of Awesome Turbofan Wheels