The oldest and simplest type of bicycle is the "fixed gear" bicycle. This is a single speed bike without a freewheel i.e whenever the bike is in motion, the pedals will go around - there is no coasting on a fixie.
There is a purity and simplicity to the fixed gear bike that can be quite seductive and it provides many benefits. When you ride a fixed gear, the need to push hard to get up the hills forces you to ride at a higher intensity than you otherwise might – making you stronger. When you descend, you can't coast, but the gear is too low. This forces you to pedal at a faster cadence than you would choose on a multi-speed bicycle. High-cadence pedaling improves the suppleness of you legs and the high rpm's force you to learn to pedal in a smooth manner.
A fixed gear gives you a very direct feel for traction conditions and this same feel for will help you learn exactly how hard you can apply your front brake without quite lifting the rear off the ground.
A properly set up fixed gear with its perfectly straight chainline and absence of derailleur pulleys marks a real improvement in drivetrain efficiency – one that you can definitely feel.
Many people find a fixed gear bike too daunting so opt for a singlespeed, freewheeling hub, that offers many of the advantages of a fixie but enabling you to coast.
Hubs are available that are “flip flop” - in that they offer both single speed on one side and fixed on the other. You can easily spin the rear wheel over to ride either "fixed" or "single speed".