Click to expand for best view.
Here are some pictures from the Wikipedia site. First a picture of an iron oxide mix. There are other mixes possible with other metals but a mix of iron oxide (rust) and aluminum powder will produce the highest temps. and most volatile reaction.
An iron oxide mix being ignited. It is often compared to black gun powder (but hotter I think).
Here, a rail joint is being welded. The pot assembly is clamped to the rail joint and the mix ignited, It quickly burns its way down to the joint depositing molten metal and welding the joint together. The pot is lined with a high temperature ceramic to withstand the heat. There is a good write up on the process in a Lindsay reprint, that I can't find right now.
A welded joint. Looks rough but when cleaned up is as strong as the rest of the rail.