Arguably one of the most common questions posed by those unfamiliar with kiteboarding is, "Does it take a lot of strength?" The default answer is 'no', as that question is almost always in reference to the process of attaching yourself to the harness, which alleviates much of the pull on your arms. In reality, kitesurfing does require power, along with core strength, balance, coordination, and stability. If your aspirations are limited to merely riding, then physical fitness will have very little impact on your riding (minus your weight, which requires larger kites and kiteboards). If you want to jump, surf, or pursue any loftier feats, physical prowess is crucial for success.
Like any sport, the more practice you put into kiteboarding, the better your riding will be. One factor that is so often overlooked though when bettering your kiting ability is preparing off of the water. While this can certainly involve trampoline training for building muscle memory and spatial awareness, your kiteboarding can be greatly enhanced by basic exercise and stretching.