Beaten egg whites are folded into batter to create a light and fluffy texture. When you beat egg whites until their color turns white, you create air bubbles. The purpose of folding is to retain those air bubbles in the batter mixture. Because the beaten eggs can settle rather quickly and the bubbles can go away, make sure all other ingredients are already mixed in and that this is your last step right before cooking. Also, eggs at room temperature whip better than cold eggs. To fold eggs, first gently pour the beaten egg whites on the batter. Use a rubber spatula to cut down the middle through the mixture and move the spatula across the bottom and up the side, bringing some of the mixture from the bottom to the surface. Turn the bowl one-third of a turn each time until you complete the process.
When making and folding an omelet, always cook on low heat. The omelet will not uniformly cook on high heat (the bottom will burn and the top will be too runny to stay together when flipping or folding).
Folding food can be effective, but it does not mean it is the easiest method. For instance when making deviled eggs, mix the yolks and combine with all other ingredients in a zip lock bag and squish them together (many recipes call for folding the ingredients into the egg yolks but I think this works better). Once the ingredients are mixed together thoroughly, cut a small hole in the corner of the bag and squeeze to fill your eggs.