why do elves need to go to the undying lands?

[stevensimth3675g]

Elves are indeed immortal in the sense they won't die of old age, but they can die from grief or severe wounds. The journey to the Undying Lands allows them a peaceful existence without these woes. When Elrond talks about his daughter's "death", he means her choosing a mortal life with Aragorn, which will eventually lead to her physical death, something Elves aren't accustomed to. It's a metaphorical death from his perspective as an immortal being.