Using a double boiler or a small saucepan, combine the sugar, salt and water. Stir until dissolved.
Bring to a boil over medium-low heat and cook until it reaches soft ball stage, or 234℉ on a candy thermometer. DO NOT stir once it begins to boil, or the sugar will crystallize (the mixture should not be grainy if you rub a small amount between your fingers - if remains grainy after it reaches 234℉, cook for 30 seconds - 1 minute longer or until the sugar has dissolved).
While the mixture is cooking on the stovetop, combine the egg whites and cream of tartar in a large bowl or the bowl of a stand mixer. Beat the egg whites on high until they form stiff peaks.
Remove the sugar mixture from the stovetop and slowly pour into beaten egg whites; continue to beat until frosting is thick and fluffy, around 7 minutes.
Add vanilla extract and continue to beat 30 seconds minute longer. Use immediately to ice cake, before it sets.