Handfastings are so called because, in many marriage ceremonies, the joining of hands is an integral part. In some European handfastings, the hands of the pair were cut and then bound together so that their blood intermingled - a worldwide sign of the joining of families.
Handfastings may or may not be legal in the eyes of the law, depending on what the couple wishes. The only difference is whether they decide to go through normal legal procedures for their locality (blood test, marriage license, a legal minister) or not. A couple may not wish to for several reasons. The handfasting may not be meant for a lifetime commitment. They may feel no reason for the law to interfere with a purely spiritual commitment. The person they wish to handfast them may not be legally recognized as a cleric. Or the handfasting may not involve one man and one woman and therefore will usually not be legally recognized.
Some people choose to commit to each other for a year and a day, after which time they may renew the vows, make a commitment for the rest of their lives or just decide to go their seperate ways.