He was Gil Galad's herald in his army. Elrond and his twin Elros were born of Earendil and Elwing, and were the great grandchildren of Beren and Luthien thus the half elven attachment. Beren was human and Luthien an elf born of an elf and a Maia.
There are many secondary reasons that Elrond received Vilya, such as the fact that he was Gil-Galad's herald and second-in-command, and Galadriel already possessing Nenya before Gil-Galad's passing, but the primary reason is because Elrond is Gil-Galad's heir.
What is the relationship between Galadriel and Gil-galad?
Gil-galad is the GRANDSON of Galadriel's brother, Angrod. So Galadriel is Gil-galad's Great-great aunt. Her hair shine with the light of the Two Trees of Valinor which where destroyed more than a millenium and a half before his own birth.
Tolkien considered several different parentages for Gil-galad in different draft texts, including making him the son of Orodreth. In the second version of The Fall of Númenor, he is called a descendant of Fëanor, who made the Silmarils. Then Tolkien treated him as a son of Finrod Felagund.
Gil-Galad was probably a better fighter than Elrond too. One of the High King's greatest feats was leading his people during the Last Alliance of Elves & Men, then battling Sauron two-on-one with Elendil.
No question: Gil-Galad was a king, and he had the ring Vilya, most powerful of the three. He was so powerful that his forces, along with Elendil's remnants from Numenor, were able to defeat Sauron even while he had the One Ring.
Elrond's powers are great, to be sure, but Galadriel is simply in a class of her own, and is definitely the being who is greater in power between the two of them.
Gil-galad was the last heir of the kings of the Noldor in exile, and acknowledged as High King of the Elves of the West. Many Elves, both the Sindar and the Noldor, joined him. But soon, there was again unrest among the Noldor, and many of them left Lindon.
Gil-galad was the last High King; after his time the title is never used. In order of succession, the Kingship would presumably have fallen on Turgon's descendants; Eärendil (who was in the West and could not exercise it) or his eldest son Elrond (who never made claim to the Kingship).
It is a reward of high honor for Galadriel and her team of soldiers, as a recognition for their bravery in chasing the evil Sauron into the North to discover if his poison and malice still existed in the world.
Fans know from the later Lord of the Rings and The Hobbit tales, that Galadriel eventually finds, falls in love with, and marries Celeborn, the elf who accompanies her down the stairs when the fellowship first arrives in Lothlorien.
First off, Galadriel was the first cousin of Turgon, who was Elrond's great-grandfather, which made them first cousins thrice removed. Furthermore, Elrond was the great-great-grandson of Galadriel's uncle, Fingolfin.
Gil-galad wanted mithril because the Light of the Eldar was fading in Middle-earth, and the Elves along with it. They required the light of the Silmarils to save themselves, but they never needed to look underground for salvation.
How Gil-galad and Elendil Defeated Sauron. In the books, Sauron was already defeated when Isildur cut the One Ring from his hand. So, what actually happened? The Silmarillion says this: "[Sauron] wrestled with Gil-galad and Elendil, and they both were slain, and the sword of Elendil broke under him as he fell.
Why were Galadriel and Cirdan not invited to the Council of Elrond? Galadriel was tied to Lothlorien not only as the ruler of that realm, but her ring Nenya preserved the purity of that land and helped protect it from the threat of Orcs.
Summary. Galadriel is portrayed as much more powerful than Elrond in terms of magical abilities and feats of strength in The Lord of the Rings and The Hobbit films.
Gil-galad was the last High King; after his time the title was never used, as he fathered no children and no obvious heirs of the House of Finwë remained in Middle-earth. Galadriel of the House of Finarfin perhaps had some rights, but did not claim them.
Galadriel, by a long, long way. She's essentially the most powerful non-angelic being in the setting by the end of the Third-age. About the only feats we have that are comparable between them (they have very, very different skillsets, so far as we see) both come in Return of the King/Appendices.
Celebrían was an Elf-lady of Lothlórien, the daughter of Celeborn and Galadriel. As the wife of Elrond, she was also known as Lady of Rivendell. She was the mother of Arwen and the twins Elrohir and Elladan.
In LOTR, Elven heirship operated under the tradition of "agnatic primogeniture," which meant that only sons through the male line could become king. Elrond was an Elvish prince, but he didn't quite fit those parameters. High King Turgon was Elrond's great-grandfather, but that was through Turgon's daughter Idril.
In The Lord of the Rings, it is said that had Galadriel chosen to use her powers for evil instead of good, she would have been even more destructive and terrifying than Sauron himself. Galadriel was the greatest and most powerful of all Elves in Middle Earth in the Third Age.
While Glorfindel already one of the greatest of all elves as Ecthelion and Glorfindel are Gondolins greatest captains. So in the first age Feanor is the most powerful elf. In the second age it's Galadriel. In the Third age it's reincarnated Glorfindel.
Unfortunately, Elrond's host arrived too late and was not large enough on its own to defeat Sauron's army. He retreated north with the refugees of Eregion, including Celeborn, only escaping because the forces of Durin III assailed Sauron's army in the rear.
