Hi Scott, thanks for reading and commenting.
When a person burns their skin, the flesh absorbs some of the heat. Unless they cool the area immediately, the skin will continue to burn - much like an egg continues to cook after you remove it from boiling water.
Putting greasy substances like butter or oil on the burned area will slow heat release from the skin. Butter may also contain bacteria, and burn injuries are particularly prone to infection.
"Directs" may have been a better word choice than "drives." I mean that if the heat can't escape from the skin's surface because of the butter or oil, it will move inwards instead.
People use many different substances on burns, including soy sauce, mustard, toothpaste, fish skins, and butter. However, organizations such as the Red Cross, which offer first aid courses and advice, do not recommend any of these. I hope this helps.