This is usually done with panning. You track the moving subject with the camera during the exposure, matching its motion as smoothly as possible. Because the camera moves with the bike, the rider can stay relatively sharp while the background blurs sideways.

A slightly slower shutter speed than you’d normally use helps create the motion blur effect. It takes practice to find the right speed and to keep the subject framed and in focus while following it.

Good practice subjects are runners, cyclists, or children playing—anything moving predictably. Even if you’re not trying for dramatic blur at first, simply following the subject helps you learn the motion.

Other ways to create a similar look include mounting the camera to the subject so the subject stays fixed relative to the camera, adding background motion blur in post-processing, or using a zoom burst at slow shutter speeds. But for the classic sharp subject / blurred background look in-camera, panning is the main technique.