The reason for adding fertilizer is pretty simple. Fish eat many types of aquatic invertebrates. These are bugs that exist in pond settings. The bugs need something to eat to get fat for the fish, and that something is algae.
Planktonic algae
The algae that serves this purpose best, is phytoplankton. This is a simple, single cell organism that grows in suspension in the water of ponds and lakes. The nice blue green tint in the water is what you are after. In fact, you want it to be dark enough that you can not see an 8 inch black and white disk at a depth 18 to 24 inches.
Fertilizer
The fertilizer you need to use, should be high in phosphorous, and low in the other two main ingredients.