Combine water and sugar in a large saucepan, and bring to a boil over medium-high heat, stirring occasionally. Add apricots; bring to a boil. Cover, reduce heat, and simmer 10 minutes or until apricots are tender. Place apricot mixture and vanilla in a blender; process until smooth. Chill.
Pour mixture into the freezer can of an ice cream freezer, and freeze according to manufacturer's instructions. Spoon into a freezer-safe container; cover and freeze 2 hours.