I didn't really know what practical uses it could have until I started playing around with it and then I found out just how useful it could be!
It is a really handy and easy to use tool which as it makes things darker, also brings out their detail a little bit more. It works in exactly the same way as the dodge tool, except you just have to press ctrl as you're using it to get the burn tool rather than the dodge tool.
The effects can be subtle or obvious depending on how many times you go over the area that you want to darken. You can easily darken a whole picture or simply selected elements that you want to bring forward a little bit.
(It was a really foggy day!)
The burn tool in GIMP is a really clever thing, I don't quite get all of the uses it could have yet, but I am sure I will get there.
Related Post: The GIMP clone tool