There are a few reasons that people might tape down their back windshield wiper. The most common reason is to prevent the wiper from leaving streaks or smears on the windshield when it's not in use. When the wiper is left up, it can sometimes catch wind and blow around, which can also cause streaking. Taping it down prevents this from happening.
Another reason people might tape down their back windshield wiper is to keep it from freezing in place during cold weather. If the wiper arm is left up, water can collect on it and freeze, which can damage the arm or make it difficult to move when you need to use it. Taping it down prevents this from happening by keeping water off of the arm.
Finally, some people just prefer the look of a taped-down wiper! It can give your car a neater appearance, especially if you have a clear windshield cover (like those made by Rain-X) that covers the entire wipers area when they're not in use.