Tar-Elestirnë was a title given to Erendis after her betrothal to Aldarion. Some time before this, Aldarion had given Erendis a diamond, a gift he had brought back from his journeys to Middle-earth. Erendis had the jewel set on a silver fillet, and when their betrothal was announced, she wore the diamond on her forehead. From that time on, she was given the title Tar-Elestirnë, Lady of the Star-brow.
Erendis does not appear to have worn the fillet indefinitely - there are signs that she abandoned it after her estrangement from her husband. Nonetheless, the tradition had been set, and the later Kings and Queens of Númenor wore a fillet of this kind in place of a crown. The tradition survived into Middle-earth after the Downfall: the Kings of Arnor wore the Elendilmir, a royal jewel in the same style as Tar-Elestirnë's gem.