The effect of this gearbox is to make the wheel rotate at various different speeds or gear ratios, compared to the sprocket mounted upon it. Most hubs also have a normal or direct-drive gear in which the sprocket drives the wheel directly (i.e. they rotate at the same speed). In this gear the internal parts are just idly turning and the hub is most efficient. When other gears are engaged however, those tiny internal cogs rotate under load and a small amount of motive power is lost in friction. These losses are a bit higher than clean and well lubricated derailleur gears, and tend to increase as the internal ratio departs further from 1:1. But a clean and well lubricated derailleur transmission is a rare thing!
There are clearly some advantages in enclosing all the moving parts required to change gears together with their lubricant, and protect them from dirt and the weather inside the rear hub shell. For that reason, internal gears are best on cycles that must function reliably and efficiently in all weathers, every day and without too much attention. A chaincase can easily be fitted to an internally geared bike and adds the finishing touch for easy-care cycling.
Another kind of internal gear is built into the bottom-bracket and chainwheel, and makes that rotate at a different speed compared to the pedals. Since pedals turn slower with more torque than wheels, bottom-bracket gears need to be stronger than hub-gears. They are rare and expensive, but a good way to boost the gearing range when multiple chainrings cannot be fitted. The only manufacturer is currently Schlumpf Innovations. Several different models are made, all two-speed: direct-drive plus either a step up or down.
It is also possible to combine internal with derailleur gears, usually a hub-gear and rear derailleur. This arrangement tends to combine most of the disadvantages with only some of the advantages of both systems, but enables a wide range of gears to be provided on designs of bicycle where it is not convenient to mount a front derailleur.