Here's an example...
This first image was taken at a relatively fast shutter speed of 1/1600th sec. and it freeze the bicycle to the point that it doesn't look like it's moving at all and you can inspect the spokes on the wheels and see no motion blur.

2W0A0733.jpg by
Tim Campbell, on Flickr
This image was taken at a deliberately slow shutter speed of just 1/40th sec. At that speed the rider would have been completely blurred (they were moving too fast) but instead of keeping the camera steady, I'm "panning" the camera as the bike rides past me so that my lens is attempt to move at the same speed as the rider. Of course this won't be perfect so I'll hedge my bets by using the "continuous burst" shutter mode and blast off a dozen or so shots and inspect them. Many will not have tracked perfectly and will be discarded, but a few will have tracked perfectly and you get a nice sharp rider with blurred wheels and a blurred background. (this is basically "lucky imaging" where to blast off lots of shots and hope that a few are keepers. As you get practice at doing this the keeper rate improves.)

Panning Shot of the Trek Madone Race Shop Limited by
Tim Campbell, on Flickr
You can see that the 2nd shot definitely helps the viewer capture the feeling of "motion" even though this is a still image. The first image has a frozen rider and it looks as though someone welded the bike to the ground so that it wouldn't fall over.
If you want to learn the panning technique you can probably find a few YouTube / Vimeo videos that walk you through the process. It's fairly easy and mostly it's all about practicing being steady as your rotate your body to follow the subject.
I find that in the beginning it helped to start with a faster shutter speed... maybe 1/125th... which is enough to get some blur... just not as much ... and then work your way down toward slower and slower speeds until you are comfortable enough doing it as slow speeds which create a lot of motion blur.