Ghee is clarified butter, like what they use in India. The butter is clarified by a special process which removes most of the casein (milk protein) and lactose and I know lactose-intolerant people who eat it. I use ghee for cooking, since it is very heat-stable as opposed to olive oil. I add olive oil after cooking or take it with salads. Ghee looks a bit different than butter, not white-yellowish, but rather yellowish-transparent. It’s basically just the fat of the butter. It can be conserved for a long time, you don’t even have to put it in the fridge.
This is a recipe on how to make ghee (I have never made it myself though and I think it’s not that easy): http://www.ayurveda.com/online_resource/ghee_recipe.htm
Hope that helps.