The figure eight is an aluminum or steel device in the shape of an eight. The small loop is attached to a carabiner on the harness. The rope goes through the large hole, around the neck of the figure 8 and back through the large hole. When it's all rigged up, its better if the rope is on top of the neck to help prevent a girth hitch from forming. The recommended way to attach a figure 8 is as follows.
The figure 8 dissipates heat quickly. It is easy to attach and inspect. It works with single strand (not very much friction) or double strand (a good amount of friction). Some figure eights can be locked off by bringing the brake strand over the head and between the figure 8 and the rappel strand. Figure eights are relatively cheap - I bought mine for $10 in 2010.
The figure 8 imparts a twist on the rope, which can make it very hard to retrieve the rope.
There is only one friction setting.