One-third of the nutrients in a potato lie just below the skin. Potato peels are full of elements that are useful as fertilizers for plants, but they are not necessarily ready as they are. The nutrients in a potato lie mostly in the skin while the vitamins are in the flesh of the potato. Nutrients like nitrogen, potassium, phosphorus and magnesium are all necessary for plant growth, while the starchy carbohydrates are food for the microbes in the soil.
The nutrients in the potato peel need time to break down in the soil before they are available to the plants as fertilizer. Ground potato peels in a solution of water sprayed over fields in the fall have time to decompose before the spring crops grow.
Compost is the simplest way of making potato peels into fertilizer. If you mix them with other household waste like vegetable scraps, eggshells and paper, they decompose into a crumbly, dark soil after three or four months. The composted potato peels are excellent fertilizer for your plants.
Undecomposed fresh potato peels are full of sugars. If you toss them around your plants, not only do they smell bad as they decompose, but also the high starch content invites fungi, bacteria and bugs around your plants. The only way to effectively use the fresh peels directly in the garden is to bury them -- although you run the risk of new potato plants sprouting up from the eyes in the potato peelings.