Butterfly locs are a style of faux locs (cf. dreadlocks) that are not actually 'locked', but have, very broadly speaking, the same sort of look. A hairstylist takes synthetic braiding hair and wraps it carefully around braids of natural hair; while the effects vary, the general appearance is of long tight ringlets with artistically-messy irregularities giving boho-chic look.
The visible loc is actually a wound wrap rather than a braid, with small loops of wound hair pulled out to give a an irregular, full-bodied texture. The end result is more regular and tighter than a traditional loc, but kinked and and with more body than traditional braids. They are generally worn long, but butterfly bobs are also fairly common.
While the primary purpose of butterfly locs is fashion, they also have the benefit of entirely protecting the natural hair within. The hair will still need to be oiled, and the locs themselves will need to be protected as will any extension. Removing the locs is done by cutting the tips (where no natural hair should be damaged), and carefully unwinding.
When the same 'butterfly' effect is done with a braid rather than a winding wrap, the style is often called Boho braids. Butterfly braids generally refer to a different style, in which tightly pulled roots give a 'winged' backdrop to thick braids.