When photographers say "panning", what they mean is that you would use a relatively long exposure time that will invariably cause some motion blur, while at the same time you'd be following the subject as it moves across your field of vision and would (hopefully) be keeping it steady in the viewfinder so as to have it remain sharp against the moving background.
The trick is to practice. Get to a place where you have enough room to frame your subject in your viewfinder, even at its point of closest approach, then, as the vehicles, animals, runners or anything else you decided is going to be a great subject for this sort of shot passes by you, rotate from the hips so as to follow it's trajectory with the front of your lens. The subject should stay pinned to the same area of your image for the duration of your shot, so it's important to try and match its speed as it passes by in front of you - this is the tricky part, as it's extremely easy to loose sync and turn slower or faster than your subject moves, resulting in a blurry subject - less than ideal.
A few months ago I realized I knew, in theory, what "panning" meant, I knew how one is supposed to do it, but I had never tried anything like it.
So when I was offered the opportunity of shooting this motorcycle club on an outing while I was in Sanya, Hainan - China, I jumped at it - knowing that this was just the sort of photography they would appreciate - as it's not something one can simply go out and do with their phone, it requires if not the best equipment there is, certainly some knowledge and a lot of trial and error - at the beginning at the very least.
So here I was, out of my comfort zone, dangling on the back of a motorcycle (moving motorcycle) or a car, or just standing by the side of the road, trying to do photographs like I'd never before tried.
It was certainly a new experience. Just to make this clear, my equipment is great and all, it just isn't the type of equipment one uses for motor sports photography. By that I mean that I had portrait lenses, not stabilized, no zoom - 85 mm, 100 mm, 135 mm, and wide angle lenses - 24 mm, 35 mm.
The end result, while quite hard to achieve, was impressive - at least to me and the people I photographed, but neither them nor I knew much about motor sports photography.
After this experience, I decided I could apply this sort of technique to lifestyle photography when I was in The Grand Velas in Nuevo Vallarta, Mexico - here are the results: