A fixie (or fixed gear) is a bike without a freewheel and only one gear ratio. You can't coast or shift on these bikes. Over time fixed-gears have gained a certain, perhaps unreasonable, cult status among some cyclists.
Fixed gear bikes are often constructed with a flip-flop hub in the back that allows for switching to a freewheel mode. Lots of folks coast through the city on single-speed freewheeled bikes.
These have become a part of hipster chic, alongside classics like the messenger bag.
Perfect bikes for Bike Polo.