To be a bit more precise, the sugar is a substitute for the adjuncts which would normally be used to lighten beers in this style. These adjuncts, most commonly flaked corn or rice, add fermentable sugar to the beer, but have to be mashed in order to convert the starches to sugars. In an extract beer, the mashing has already been done for you, and the malt extract no longer has the enzymes needed to convert the adjuncts*, so you use the refined sugar to get the same result.
For an example of a beer that uses adjuncts, see the well-known Cream of Three Crops Cream Ale. Cream ales were originally introduced to compete with light lagers**, so they also use adjuncts to lighten the beer's body. It's an all-grain recipe, so you wouldn't be in a position to brew it yourself yet, but it should give you an idea of what an adjunct beer is like.
*There are malt extracts which have the enzymes still in them, called diastatic malt extract, but these are both expensive and hard to come by.
** If you read the comments, you'll see the term 'BMC' bandied about quite a bit. It stands for 'Budweiser-Miller-Coors', the most common beers in the US and the (low) bar by which many non-craft drinkers judge beers. It is not usually used in as positive a light except when trying to make a lighter beer