In a 2-quart top of a double boiler combine sugar, water, egg whites, and cream of tartar. Beat with an electric mixer on low speed for 30 seconds.
Place the pan over boiling water (upper pan should not touch the water). Cook, beating constantly with the electric mixer on high speed, for 10 to 13 minutes or until an instant-read thermometer registers 160 degrees F when inserted in the mixture, stopping beater and quickly scraping bottom and sides of pan every 5 minutes to prevent sticking. Remove pan from the heat; add vanilla. Beat about 1 minute more or until frosting is fluffy and holds soft peaks. This frosts tops and sides of two 8- or 9-inch cake layers or one 10-inch tube cake. Store frosted cake in the refrigerator and serve the same day it is made.