© Denzil Green
There are things that the ancient Romans made but we don't know what they actually were, as the items were so everyday in their kitchens that they never needed explaining in writing. Two thousand years from now, historians may struggle equally over our word, "cookie." Cookie is really hard to define; with any luck, future archaeologists will find a petrified example of one with a label attached and that will set it all straight.
An attempt at a definition: a small, usually crisp cake that can be eaten from the hand in a few bites. It is flat, though sometimes it may be raised slightly. It is made from a sweet dough that has been rolled and cut and then baked on a cookie sheet (flat baking sheet.) Sometimes, the dough is a bit more moist, and is dropped onto the cookie sheet by spoonfuls.
"Americans consume more than 2 billion cookies every year, translating into 300 per person annually." 
- For crisp Cookies, use white sugar. It doesn't absorb moisture from the air;
- Use a flour that could also be used for bread -- such as bread flour or Canadian all-purpose flour. The higher protein in the flour will absorb moisture, meaning less moisture is available during cooking to be turned into steam and puff up the Cookies;
- For crisp Cookies, cook a few minutes longer.
- For soft Cookies, use brown sugar or honey -- both will absorb moisture from the air and help keep the Cookies soft;
- Use a flour that is low in protein -- such as cake & pastry flour, plain flour, or American all-purpose flour. Having less protein, more of the moisture in the dough will remain unabsorbed, and during cooking that moisture will turn into steam and puff up the Cookies;
- For soft Cookies, cook a few minutes less.
If a recipe calls for some white sugar and some brown sugar, then the author of that recipe is aiming to create a cookie that is somewhere betwixt crisp and soft.
Butter, being a natural substance, contains water and so will melt as it heats, making Cookies that spread out. Shortening, being a man-made product, contains less water than butter, and so won't melt as fast during cooking, making dough that holds its shape more and thus Cookies that spread out less.
If you overbaked cookies, store them in an airtight container overnight and they will start to soften.
Cookies is more of a North American word. They are called "biscuits" in the UK, though the North American word is starting to make inroads.
Literature & Lore
The word "cookie" may come from the Dutch word "koekjes", passed into English through the Dutch settlers in New York.
In Latin, "that's how the cookie crumbles" is "sic friat crustulum".
 Bakery 2010 White Paper - Innovative Insights for Fall Promotions" insert in Baking Buyer, March 2010, Vol. 5, No. 2, Page 18.
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Biscuits (French); Biscotti (Italian); Bizcochos, Galletas, Pasteles (Spanish); Biscoitinhos, Bolachas (Portuguese)