Each time you go through the line (once an hour) you can get an entrée and a drink, and then you also get one of the following - either a side or a dessert. You just have to pick between the side or the dessert. Keep in mind that many of the meals already come with a side, so if you get one of those meals you can also then select a dessert. So at Mango Joe's the Bacon Cheeseburger is advertised as "served with fries" which means you can still select a dessert at the same time, or if you wanted an additional order of fries you could get that instead of the dessert.
In your example you could select a burger and fries, and then an hour later you could then go through the line again and select a burger and a dessert. It is not specifically that you have to wait an hour for dessert, but just that you can only select one out of the options of a side or a dessert, and that you can only go through the line once an hour.