I'm not really sure. All I read was that the twigs they planted were dormant.. when they start to grow they root themselves and go all pretty like that. I know that when my nephew was born, my aunt got his mother a flower arrangement that had twigs in it called Parking Willows (my nephew is named Parker, hence her picking them). After they were done with the arrangement, they planted the twigs and it bloomed into a great big tree really quickly. Maybe it's the same kind of concept.
Willows are probably THE easiest of all plants to root, usually just sticking them in the ground is good enough (just make sure that you place the end that was originally closest to the dirt into the dirt... in other words, don't turn them upside-down or they'll likely never root).