When a fat or oil is heated to its smoke point, several things occur. 1) the fat or oil begins to break down into glycerol and free fatty acids 2) flavor and nutritional value begin to degrade, and 3) smoke forms, irritating the eyes and throat.
Each fat and oil has its own particular smoke point and lend themselves better to different cooking methods. For instance, the smoke point for ghee is around 500 degrees which is ideal for high heat cooking like frying or broiling. Sesame oil on the other hand has a much lower smoke point and is better for salad dressings and dips.
If you are interested in exact smoke points for several common oils, check out the nitty- gritty about smoke points here. If you prefer a more visual representation of the smoke point and best use case for a variety of oils, check out this awesome chart from Chasing Delicious.