The Undying Lands are the final resting destination for Bilbo and Frodo in places like Valinor serve a deeply important role in the mythology of The Lord of the Rings.
Valinor serves as many things in the full scope of The Lord of the Rings, both as a physical location and as a metaphorical plane outside of the primary setting. This unique history and specific quality to the inhabitants of that land make it one of Tolkien's most important settings despite rarely actually appearing in the stories penned by the author. Here is the origin of the Undying Lands otherwise known as Valinor, why they're so important, and who is allowed to reach that land.
The Undying Lands Is Home To Tolkien's Valar, Maiar, & Elves
Only A Handful Of Characters Can Reach Valinor
One of the most important places in all of J.R.R. Tolkien's mythology, the Undying Lands known as Valinor are an ethereal and unseen location in the universe of The Lord of the Rings. The Valar are a race of angelic figures in the Tolkien cosmology. Following their conflict with Melkor, the Valar relocated to Valinor, far off the western shores of Middle-earth. This land also became the home to the Maiar, lesser beings of great power who went to Middle-earth in the form of wizards. While Elves can sail to these lands and make their home there, most others can't.

If Valinor Is West Of Middle-earth, What's To The East?
As seen in LOTR: The Rings of Power, Valinor is directly west of Tolkien's Middle-earth world. Here's what's on the eastern side of the map.
The Undying Lands serve as the final home for the more ancient races of J.R.R. Tolkien's cosmology, with Men, Hobbits, Dwarves, Orcs, and the Ents incapable of reaching those shores. However, there are a few notable exceptions. In honor of their sacrifices, Ring-Bearers like Bilbo and Frodo are allowed to travel to Valinor alongside Gandalf at the end of The Return of the King. The appendices of the trilogy later penned by Tolkien reveal that two other characters followed them: Samwise (due to his status as a Ring-Bearer, if even only briefly) and Gimili (who traveled to Valinor alongside Legolas).
Where The Undying Lands Is Located & What Purpose It Serves
Home To Some, Heaven To Others
The Undying Lands are far to the west of Middle-earth. As expanded upon in other stories collected together as The Silmarillion, the Undying Lands are located on the distant continent of Aman. This land was protected for a time, until the Valar attempted to confront Morgoth after the awakening of the Elves. The conflict between the Valinor and Morgoth, as well as the hubris of Númenor, resulted in the flat world of the 2nd age being converted into a round planet during the 3rd age. In the process, Aman (as well as Valinor) was severed from the rest of the world.
For characters like Frodo and Bilbo, the Undying Lands could be seen as a metaphor for heaven or paradise
Elves may still travel to Valinor, making the Undying Lands a literal continent populated primarily by beings who shall never from natural causes like the Elves or the Valar. However, for characters like Frodo and Bilbo, the Undying Lands could be seen as a metaphor for heaven or paradise, a final reward for their work protecting Middle-earth from falling under the sway of Sauron. There has been plenty of debate about the subject, but the Undying Lands in Lord of the Rings serve as a final resting place for some of the most important characters in the story.