A frenum is the attachment between the gum and some moving soft tissue part of the mouth - typically the tongue (lingual frenum) or the lip (labial frenum).
Sometimes this is contributing to a problem with the gums or the alignment of the teeth - particularly when the frenum is attached to the gum right at the level where the teeth emerge. Maxillary labial frenum is capable of creating a diastema and recession, affecting aesthetics.
The most common reason for frenectomy is orthodontic treatment, sometimes for dentures. In this case, the gap between teeth had already started closing after surgery.