I am making the following recipe for a birthday party: Pinata cookies!, and it calls for cream of tartar in the dough. This is the first time I've seen that in a cookie recipe and I can't figure out what the purpose of it is. Anyone know what cream of tartar does in baking recipes?
As @rumtscho said, it is an acid and in your recipe above it is for activating the soda.
However, in general, recipes almost never call for cream of tartar for this purpose. Modern recipes, if they need acid to activate the soda, will call for baking powder instead which has the cream of tartar already mixed in.
Almost every time I see cream of tartar called for in a recipe it is when making a meringue. The acid denatures some of the egg white proteins and makes the eggs froth up faster and makes a stiffer meringue. Cream of tartar is good for this as it is dry so it doesn't throw off the liquid content and it has little flavor of its own.
It is a weak acid. It purpose is to react with the baking soda for leavening. If you can't get it, you can use some other acid, e.g. citric acid, but it will introduce a slight taste of its own, and it is stronger than cream of tartar. You can also substitute baking powder instead of the baking soda + cream of tartar combination.