Capturing visible motion in photography isn’t new. You can see hints of it in very early analogue images, but it was often the result of the limited technology at the time so it wasn’t actually done on purpose!
Chances are, you’ve seen a lot of intentional blur photography in modern times. The most popular example is waterfall photography, where photographers go to a lot of trouble to capture the cascading water in a soft, dreamy blur, while making sure the rest of their image is sharp and still. It’s a signature of that style of photography, and the reason why we’re all so drawn to pictures of waterfalls
Car photography is another good example. In many cases, photographers use a technique called panning, which involves using a slow shutter speed to achieve a blurry finish. Instead of keeping the camera stationary, the camera moves alongside the subject as it passes. The result? An image with a sharp subject (aka the car), and the background blurred by motion.