There are many types, different makers and as with any tool varying price points from the cub at $70 to, say, the top of the line models in the $450-$700 price ranges. Those we will relegate to the professional wood carvers who need them.
Okay, but I am getting ahead of myself. A wood burning pen is just that: a pen-like device with a specialized tip and a control module that regulates the heat, that you use to burn designs, textures, or pictures into wood. There are many different shaped tips available which all do assorted jobs: half moons used for burning in scales on dragons or fish; fine pointed tips for drawing delicate lines for feathers on birds; or round circles for burning in eye sockets.
There are even custom made tips that can burn in your signature perfectly each time, most dealers carry an assortment for you to choose from. The module for the pen is just a small box with a transformer inside to regulate power, an on/off switch on the outside, with a dial to regulate how much heat you want going to the pen tip. The dial called a rheostat dials in how much electricity goes to the tip of the pen, and thus how hot it gets.