In a medium saucepan combine water and sugar. Bring to boiling, stirring to dissolve sugar. Remove from heat; cool 30 minutes. In a 2-quart square baking dish, combine sugar mixture, lemon juice, and tarragon. Cover and freeze about 7 hours or until nearly firm.
Break frozen mixture into small chunks. Transfer to a chilled large mixing bowl. Beat with an electric mixer on medium speed until fluffy but not melted. Return mixture to 2-quart square dish; cover and freeze at least 3 hours or until firm.
To serve, let stand at room temperature for 10 minutes. Using a large spoon, scrape across surface and spoon into dessert dishes. Makes about 6 cups (12, 1/2-cup servings).