Sugar alcohols are a kind of molecule that has some characteristics of a sugar molecule and some characteristics of an alcohol, with a sweet taste. They do have some calories, but not as many as sugars (sucrose has 4 calories per gram, and the sugar alcohols range from .2-3 calories per gram, so depending which you are using, you can see a significant calorie savings or not much of one at all).
One of the reasons sugar alcohols are used in sugar free products (other than reducing calories) is to reduce the glycemic index (effect on blood sugar) of the food. All sugar alcohols have a lower glycemic index than sugar, though some are also less sweet than sugar and so don't result in a net savings at all, and the different sugar alcohols vary in glycemic index as well.
The major issue with sugar alcohols is that they aren't completely digested (which is part of why they have fewer calories than sugars). That means they end up in your intestines, where they can cause a lot of gastrointestinal upset that you want to avoid. People have differing levels of tolerance for side effect free consumption, so you have to experiment a bit to find the levels that are right for you. Typically, erythritol is the only sugar alcohol that isn't subject to these side effects, because of the way it is digested (it also has the lowest glycemic index and lowest calories per gram).
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