Panning means moving with your subject, so that the subject appears to stand still while the background appears to move. Like in the picture above.
To do this, you use shutter speed priority on your camera (“S” or “Tv” mode) and select a shutter speed of around 1/8 – 1/30th second. Move with your subject, and shoot in mid-move (keep moving after your picture is taken).
Then shoot repeatedly: not every image will work.
But you don’t even need to wait for moving subjects: create your own. For even more fun, here’s a tip: try to do this while you are zooming in or out with your zoom lens, instead. No, not all the time – everyone will think you had too many of those mushrooms – but an occasional psychedelic picture can be interesting. Like this one: