They are tough, clear plastic 'aligners' (moulds) that are used to straighten teeth. Several sets of specially moulded, slightly different aligners are made for each patient. Each set is worn for two weeks before being replaced with the next one. They are made from clear plastic, so they are nearly invisible.
Once the treatment is finished the teeth need to be held in position for a time. This is called the retention' period, and the appliances that hold the teeth in place are called retainer.