The Waters of Tyne really do exist! they are where the North and South Tyne meet. When the river is flowing heavily, the river becomes very wide and deadly. When this song was written (17th century?), there was still a ferry to take you from one side of the river to the other but in storms, the river was usually far too dangerous for a small boat and because of a number of losses, the ferries just didn't go. Hence the young woman wanting to meet her lover on the other side of the river and trying to find a boatman. The background really is a true story, I guess.