Saurabh Koranglekar
Pipes are damaged when ice forms a complete blockage, and the expansion of water trapped by it puts too much pressure on them.
Now, ice is a pretty good thermal insulator, so once a little ice forms on the inside of the pipe further freezing proceeds slowly. If the water is flowing there will not be enough time for it to freeze between leaving the (relatively warm and protected) underground run and exiting the pipe at the dripping faucet. Thus the pipe never freezes all the way through, no blockage forms and excess pressure is never applied.