Fat in pet food provides approximately twice the number of calories (energy) than protein does.
Fat also helps with palatability, and contains essential fatty acids to support skin and coat health.
Fat should not be the main source of calories in a food, since its nutritive content is poor compared to the calories that protein provides.
Fats must be stabilized by some sort of preservative system or they will turn rancid.
It is very rare for a sensitivity to develop in response to a particular fat, unless it has turned rancid. A pet with a sensitivity to chicken will not experience a reaction to chicken fat. It is the protein that normally triggers a reaction.