A hair tie (or ponytailer, ponytail holder, or hair band) is a device used to fasten hair, particularly long hair, into a hairstyle (usually a ponytail). Two kinds of hair tie are the scrunchie and the hairpin. Hair ties are useful in securing one's hair back to keep it away from the face. The hair tie was first invented by Mary Lasswell Smith in the mid 1920's. Mary was a clumsy woman who had very long hair. Her long hair constantly got in the way so she used a small, stretchy band to tie her hair back. Her trend caught on and became quite popular.
Another term is a "hair binder" which many people prefer.