This is the 3373rd most frequent Japanese word.
果て
"果て" means "the end" or "extremity."
Here, 果て refers to the end or conclusion of a journey (旅).
旅の果てに美しい景色が待っていました。
At the end of the journey, a beautiful scenery awaited.
In this sentence, 果てしない describes the sky as limitless or boundless (空).
その果てしない空には様々な星が輝いている。
Various stars are shining in the endless sky.
Here, 果て is used to express the concept of endlessness related to his adventure (冒険).