The puréed soup is simply food you’d normally eat solid transformed into a liquid. Why would we do this? Because the food is often better this way. A black bean soup, to my palate, is better than a scoop of black beans. Diced cooked celery root, or mashed celery root, is a nice accompaniment to braised beef, but if you want to feature celery root, you do so in a soup by cooking the celery root in an appropriate liquid, puréeing it, and seasoning it.
Sweet soups, fruit soups, are another form of puréed soup. When you have good fruit, you can simply purée and strain it. If you like cooked fruit, such as poached peaches, pears, or apples, the fruit can be puréed with some of the poaching liquid (simple syrup, white wine, and a vanilla bean/pod, for instance) for a terrific fruit soup, appropriate for dessert or, when made less sweet, a starting course.