I have to admit, that is a new phrase to me. Unfortunately it will probably soon turn up constantly in the public lexicon, like “civil union”.
In Neopaganism, and particularly in Wicca, “handfasting” is a term used for a wedding ceremony. The marriage vows taken may be for “a year and a day,” “a lifetime”, “for all of eternity” or “for as long as love shall last.” As with many Neopagan rituals, some groups may use historically attested forms of the ceremony, striving to be as traditional as possible, while others may use only the basic idea of handfasting and largely create a new ceremony. In some traditions, the couple may jump over a broom at the end of the ceremony. Some may instead leap over a small fire together.
They were, for all practical purposes, married, they just lacked the paperwork.