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One of its main (and best known) uses is to stabilize beaten egg whites by acting as a "volumizer" as well as making them more tolerant to heat. If you've beaten egg whites, you know that the result is very little egg and a whole lot of air. Cream of tartar keeps the foam airy. Do your cookies contain beaten eggs? If so, that's the reason for the cream of tartar.

The other likely possibility would occur with recipes containing baking soda. Baking soda is a leavening agent that needs an acid to activate it. (I'm sure just about everyone has had experience with the "volcano" projects in school that have an eruption caused by a combination of baking soda and vinegar.) It's often used in recipes that involve creaming butter and sugar together, because this process creates tiny air bubbles in the mixture that can be expanded by the addition of baking soda and an acid. Baking powder is basically baking soda with acids already added, but some recipes call for baking soda and cream of tarter rather than baking powder, because the baking powder generally has an additional acid that activates further leavening when the batter or dough is heated in the oven. (Most baking powders are labeled "double-action" or something similar that indicates the presence of the two different acids. "Single-action" baking powder would just be a combination of baking soda and cream of tartar.)