To fold is to combine something very gently. It is done when you don’t want ingredients to break up; you are incorporating rather than mixing.
You do it with a broad instrument, such as a rubber spatula or a large, solid spoon, rather than a fork or a whisk because you are lifting and moving.
It might be done with cooked, soft vegetables, or egg whites that you’ve just spent time beating air into — if you just stirrred the egg whites into the rest of a dish you are making, you’d collapse the little air pockets and negate all the work you’ve just done, as well as losing the desired air that the recipe needed.
To fold, you lift a spoonful of the ingredients carefully, turn it over onto the rest of the mixture, then repeat in a different spot and so on until everything is evenly combined.
It can help to rotate the bowl as you do it.