This pattern represents Arwen Undómiel, daughter of Elrond of Rivendell and granddaughter of Galadriel of Lothlórien. Arwen is also named 'Evenstar' as one of the last and greatest Elves to live in Middle-earth. She also bears a necklace called 'the Evenstar' which she gifts to Frodo to aid him to recover from the great weight of carrying the One Ring to Mordor saying -
"When the memory of the fear and the darkness troubles you ... this will bring you aid."
This design signifies the grace, strength and beauty of Arwen as well as the gift to Frodo.