What does the New Year carol mean? The website School of the Seasons gives some background:
All very interesting, and enough, I hope, to refute the suggestion of Simon Titley (who writes the blog Liberal Dissenter) that it sounds like the work of Rambling Sid Rumpo from Round the Horne.
Trefor Owen describes the context for this song in Wales. Very early on New Year's Day about three or four o'clock in the morning, groups of boys came round to the houses in the neighbourhood, carrying a vessel of cold spring water, freshly drawn, and twigs of box, holly, myrtle, rosemary or other evergreens. They sprinkled the hands and face of anyone they met for a copper or two. In every house, each room was sprinkled with New Year's water and the inmates, who were often still in bed, wished a Happy New Year. For this service and wish they were also gifted with coins. The doors of those houses which were closed to them were sprinkled with the water. The verse was sung during the sprinkling.
In certain parts of Wales this custom is called dwr newy (literally, new water). The exact meaning of the phrase, “levy dew” is unknown, although there have been attempts to trace it to llef I Dduw (Welsh for “cry of God”). This seems to be an imposition of a Christian interpretation on a much older custom. Although the fair maid is now equated with the Virgin, Owen thinks it likely that this custom derives from “an early well-cult made acceptable to medieval Christianity by its association with the Virgin and perpetuated both by the desire to wish one’s neighbour well at the beginning of a new year and by the small monetary payment involved.”