A wood burning tool is an electrically-powered tool that is used to burn marks into wood. They generally have a handle, and a metal extension that gets very hot, powered by electricity. When the metal tip is hot, it can be used to burn marks into woods.
This same tool can be used to trim threads, especially nylon and synthetic threads. When sewing by hand, sometimes little pieces of thread are left over after finishing the stitch and tying it off. In order to create a visually smooth, and clean finish, the thread can be snipped.
Since scissors can only get so close to the seam, due to the natural material thickness of the scissors, sometimes a little bit of thread fray is left behind. Burning it with a wood burning/thread trimming tool is a very easy way to get rid of these tiny bits of thread.
Just hold the tool lightly on the thread for a very short period of time, and it will burn away. Leather crafters have different preferences for finishing threads, for some, this is the leather craft tool of choice.