Celeborn is married to Lady Galadriel. Celeborn and Galadirel had a daughter, Celebrian, who would end up marrying Elrond. Thus making Arwen, Elrohir, and Elledan their grandchildren. Celeborn is the grandson of Thingol, who was a Telarian Elf, or Noble Elf.
Celeborn married Galadriel very early in the First Age. Thingol, King of Doriath, possessed a very rare necklace that all dwarves coveted. When Thingol refused to give it to them, he was killed by the dwarves. Elves of Doriath then chased and killed all but two of the dwarves that had killed their king. They made it to the Blue Mountains to rally their kinsmen. The dwarves then laid waste to the city of Doriath in a battle that saw massive losses of both elves and dwarves. Celeborn forever would now distrust dwarves.
The First Age ended with the War of Wrath and the defeat of Morgoth. Beleriand was ruined and sank beneath the Sea. Many of the Ñoldor returned to the Undying Lands with the pardon of the Valar, but Galadriel remained in Middle-Earth with Celeborn.
At the start of the Second Age Celeborn lived in Lindon, which was west of the Blue Mountains. Many of the elves who lived there, including the High King Gil-Galad, were Sindarin. Sometime in the middle of the Second Age their daughter, Celebrian was born. Also, in the middle of this age, Galadriel sensed an evil growing in Middle-Earth. Celeborn and Galadriel felt it was their duty to fight this evil.
The three wound up in the realm of Eregion, where many eleven-smiths dwelled. These elves are said to even deal with the dwarves of Khazad-dum, but Celeborn still did not trust dwarves.
The Battle of the Pelennor Fields was a battle for the city of Minas Tirith, and ultimately for Gondor, during the War of the Ring. It was the greatest battle of the War of the Ring, and indeed the largest of the entire Third Age. Major casualties resulted from this battle - including the deaths of King Théoden and the Witch-king of Angmar.
During the initial skirmishes, Legolas, accompanied by Aragorn and Gimli, went to the Path of The Dead. In there, was an undead army waiting to be set free. Only the heir to Gondor's throne could do so, which Aragorn was. He told the dead if they fought for him, he would grant them their freedom. Upon arrival, Minas Tirith had already been breached, but not outrighted defeated. The undead, along with Legolas, Gimli, and Aragorn were able to save the city and drive the reaming Sauron forces back to Mordor.