Elastic ligature is a term used in orthodontics to describe the small rubber bands that attach the archwire to the bracket. The term Elastics can also refer to a vertical elastic which is used to introduce better upper and lower bite alignment.
[CLASS I] Usually used to close spaces between the canine and the molar on the upper and lower arch.
[CLASS II] Used to correct overbite. Elastic is worn from the upper front teeth to the lower back teeth.
[CLASS III] To correct underbite a ligature is worn from the lower front teeth to the upper back teeth.
Any of the above combinations may be worn in combination to correct multiple problems. The elastics can also be configured in various shapes such as rectangle and triangle to be more effective in correcting crossbites and midline issues.
In the example below elastics were used to correct an over bite situation. The orthodontic ruberbands are attached to hooks placed on the brackets.
Before

After

Photos courtesy of ASO