They coat the flour strands and prevent them from becoming tough when moistened and stirred. While butter lends wonderful flavor to baking, it's lower melting point is what is causing the spread of the cookie during baking. With shortening, the starch in the flour has not gelatinized and has more time to set before the shortening melts, contributing to a puffier cookie. Eggs are both tenderizers and tougheners. Egg yolks contain fat, which tenderizes, and lecithin, an emulsifier, brings the water and fat phases together in a recipe for a creamier, smoother texture.
Liquids are essential to cookie recipes.
When wheat flour is moistened and stirred, gluten is formed from the proteins present. Gluten strands form the structure of the cookie, but they also have a toughening effect. Fats, such as stick butter and shortening, shorten the strands, and give you a more tender cookie. Baking soda and baking powder are the classic leaveners in cookie recipes, but beaten egg whites are also used.