"Half braids" are what I call any braided style which works primarily with a section of hair above the ears, leaving the lower part hanging loose on the neck. Dreamweaver Braiding calls this style "perfect."
Half braids are very versatile. They are great for showing off the length of long hair and also work well for doing small braids in short hair. They let the wearer's hair drape over his or her shoulders or back, and allow for more subtle braid styles.
For more pictures of half braids I've done, see my Flickr set here.