The IGH Advantage
Internally geared bicycle hubs have been around since the turn of the 20th century. Sturmey Archer, one of the first manufacturers, has continually produced hubs since 1902.
Until the early 70s, the venerable 3 speed was a popular choice for utilitarian and recreational cyclists. The bike boom of the early 70s saw a big move away from geared hubs as the 10 speed made huge inroads. In more recent times, the gearhub has seen a resurgence in popularity with the development of hubs with more speeds and greater gear range.
The 3 speed has made a big comeback and is well on the way to returning to its former glory. Fortunately, now hubs with 5,7,8, or even 14 speeds are available and gaining wide acceptance. Riders appreciate the simple, reliable operation and low maintenance requirements.
Gear hubs have several advantages. First, a single shifter with linear operation is simple to learn how to operate. Secondly, in traffic the gears can be changed while stopped, something you can't do with derailleurs. Finally, they make for a clean installation, fewer exposed parts and are shielded against the elements.
Here is a link to an excellent article written by cycling guru, the late Sheldon Brown.