Basically, a stak is, as Richard said, using more than one box at a time. This can be done a variety of ways. He is using a downloader in the ecm and "stacking" a second box on it by hooking ti up under the hood as normal. Then he takes it a little farther by adding a third box which interrups the signal output of the first one, modifies it again and sends that to the engine. A good stack can give you additional signal massaging capability and the ability to refine your engine parameters to make the best combination of power and efficiency. A poor stack will make a lot of smoke and heat and not so much power. It can also damage engine components.
-Scott