There's a chapter about the role of fats in cooking, in the book How to Read a French Fry by Russ Parsons. I'll try to summarize:
-Oil transfers heat really quickly as well as sealing in water, so the food cooks faster and more evenly, and stays moister.
-Oils and fats mainly vary in the amount of hydrogen they have in them. Fats more saturated with hydrogen are more solid (animal fats, coconut oil, etc.) They are also worse for you than less saturated fats (they increase your cholesterol). They also make a crisper crust, etc - they perform better as fats in cooking.
There's lots more, but these are the main points. The rest is dedicated to specifics about frying.