@iab is pulling your leg, because while he showed an example of a three-speed bike, it is not what a typical three-speed is. Look at it this way. A three-speed hub is one where the sprocket does not necessarily turn at the same rate as the hub. This is due to magic that occurs inside the hub. You can't see inside, so it seems like magic. The magic is explained here. If you want more information, see @Dan Burkhardt's youtube channel.

Here is my Rudge three-speed. It looks typical, except for the seat bag and the bottle cage on the handlebar. There is no derailleur. The shifter is on the handlebar, and it pulls a cable which goes into the right end of the axle of the rear hub. The cable works on the internals of the hub to activate the magic. 2nd gear makes the hub act like a regular one-speed hub. 1st gear makes the hub spin at 3/4 of the speed of the sprocket. 3rd gear makes the hub spin at 4/3 the speed of the sprocket.