[lathspell]

Elladan and Elrohir were brothers of Arwen and thus the sons Elrond and Celebrian. Celebrian is the reason of their mission.

I do know all of it in detail, but I believe it's something like this in headlines.

Celebrian, daughter of Galadriel, wedded Elrond and went to live with him in Rivendell where they had two sons, Elrohir and Elladan, and a daughter, Arwen. One day she set out with her maidens to visit her kin in Lothlorien, but was waylaid in a pass in the Misty Mountains by orcs. The orcs tormented Celebrian and her followers.
Meanwhile word of this reached her sons and they set out to rescue their mother. They did so! But Celebrian was treated and tormented so badly that she was nearly alive and didn't know anything anymore. She didn't want to live in Middle-earth anymore and took ship to Valinor (I do not know if she lived or died their).
Ever since this happened Elrohir and Elladan go out often to waylay orcs and destroy their plans. They never forgot their mothers torment and never stopped hunting down orcs.

greetings,
lathspell