Handfasting is a Pagan/Wiccan Wedding ritual, the term hand-fastening is literal. During the ceremony the hands of those being handfasted are bound using a cord. This is looped around the joned hands and then loosely tied. A Wiccan Hand-Fastening binds the couple together for a period of a year and a day and, at the end of this time they may choose to continue their marriage or go their own seperate way.
If the latter option is taken then the binding cord used for the ceremony is untied, hence the term, cutting the knot.
The ceremony itself is normally conducted by either a High Preiestess, a High Preiest or a Druid and can be performed anywhere that the couple find suitable. Due to the nature of Wiccan beliefs it is normally an outside event and timed to coincide with a full moon or a Sabbat.