Inside the plant, nitrogen is part of amino acids, which in turn make up proteins. It is also part of the chlorophyll molecule, thus it is important in photosynthesis. Phosphorus serves as the currency of energy exchange within the plant itself. Thus it plays roles in photosynthesis, respiration, cell division, cell enlargement, and many other processes within the plant. It promotes early root formation, and improves the quality of many fruits and vegetables.
Potassium is somewhat of an enigma.
It is essential for plant growth, however the exact functions within plants are not well understood. The primary function may be related to plant metabolism. It is known to be vital to photosynthesis, because it declines when potassium is deficient. Respiration increases when potassium is deficient. Combined, increased respiration and decreased photosynthesis reduces the plant carbohydrate supply.