As ice cream freezes, ice crystals separate from the liquid cream base. These crystals would normally join together into a solid mass (like a cream ice cube), but sugar molecules dissolved in the cream get in the way. In effect, this increases the time it takes to freeze ice cream because it takes longer for the ice to solidify around the sugar.
On the other hand, a high-sugar base will make the water freeze into smaller, less rigid crystals - meaning we get a smoother and creamier ice cream! Look out, though, because too much sugar and the ice won't be able to form at all, leaving you with a ice cream slush.
It's all about finding the right balance of sugar for the kind of ice cream, granita, or sorbet we want to make. Our recipes for Basic Vanilla Ice Cream and Basic Granita are a good place to start if you want to experiment!