Butter at room temperature mixes more easily with other ingredients, like sugar, and creates air pockets in the dough. If you use cold butter, it will not cream properly with sugar and other ingredients, and the air pockets will not form as easily, resulting in dense and tough cookies. When the eggs are at room temperature, they will also help the cookies to rise and become fluffy. If you use cold eggs, they can cause the butter to harden and create an uneven mixture, resulting in unevenly baked cookies.