Periphrastic writing is unnecessarily convoluted, confusing, and wordy. It’s like it wants to confuse you. A periphrastic instruction manual can make it nearly impossible to figure out how your new TV works.
Legal briefs and medical textbooks are two examples of written works that are almost always periphrastic. Your class president's speech might also be periphrastic, and so might the recipe for your grandma's favorite French pastry, if she adds a bit about the café she first had it in before telling you how long to bake it. The Greek root is periphrazein, "speak in a roundabout way," which combines peri-, "round about" and phrazein, "to express."