Literally "moon of honey", from when "moon" meant "month" (there are about twenty-eight days between full moons) and honey was synonymous with sweetness. The English word dates back to the mid-1500s, where Richard Huleot defined it as "a term proverbially applied to such as be new married, which will not fall out at the first, but the one loueth the other at the beginning exceedingly."
The tradition of the newlyweds taking a private vacation, be it for a week or a month, following the wedding did not appear until the 1800s.
This factual node was created on the one-month anniversary of my own wedding.