Brown Sugar in cookies help make the cookies more dense and moist.
Also brown sugar in cookies helps to attract and absorb the liquid in the dough when making the cookies so when you use brown sugar in the cookies it makes for a more perfect cookie.
You can use regular sugar as well to make cookies but it's best to use brown sugar.
Brown Sugar is also more hygroscopic than white granulated sugar which means it helps hold the moisture in the cookie dough much better.
However if you just have regular sugar and no brown sugar you can still bake cookies with regular sugar and they will turn out okay.
But if you want to make the best cookies it best to get some brown sugar and they will be much more tastier and more easier to chew.