Wiktionary
n. A bicycle that does not have a freewheel, and only has a single gear ratio.
Wikipedia
A fixed-gear bicycle (or fixed-wheel bicycle, commonly known in some places as a fixie) is a bicycle that has a drivetrain with no freewheel mechanism. The freewheel was developed early in the history of bicycle design but the fixed-gear bicycle remained the standard track racing design. More recently the "fixie" has become a popular alternative among mainly urban cyclists, offering the advantage of simplicity compared with the standard multi-geared bicycle.
Most bicycle hubs incorporate a freewheel to allow the pedals to remain stationary while the bicycle is in motion, so that the rider can coast, i.e., ride without pedalling using forward momentum. A fixed-gear drivetrain has the drive sprocket (or cog) threaded or bolted directly to the hub of the back wheel, so that the pedals are directly coupled to the wheel. During acceleration, the pedal crank drives the wheel, but in other situations, the rear wheel can drive the pedal cranks. This direct coupling allows a cyclist to apply a braking force with the legs and bodyweight, by resisting the rotation of the cranks. It also makes it possible to cycle backwards.
As a general rule, fixed-gear bicycles are single-speed. A derailleur for gear selection would introduce chain slack, which would interfere with braking. Gear selection can, however, be accomplished with the use of an internally geared hub. For example, a Sturmey-Archer fixed-gear 3-speed hub is a fixed-gear multi-speed arrangement. Most fixed-gear bicycles only have a front brake, and some have no brakes at all.