What does cream of tartar do 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.