He might gain enhanced perception. This could allow him to see chakra flow more clearly, similar to how the Sharingan can. So in battles, he can anticipate his opponents' moves better.
It might be related to a connection with some powerful entity in the Wave arc. For example, if there's a secret shinobi from the past whose power is tied to the Rinnegan and Naruto somehow forms a bond with that power source, it could lead to the awakening. Also, the intense emotions and challenges he faces in the Wave arc might be a catalyst, pushing his chakra to a new level and awakening the Rinnegan.
It could be a water - based kekkei genkai. Since the Wave arc has a lot to do with water, it would make sense for Naruto to awaken a kekkei genkai related to water. This could give him an edge in battles, especially in the Wave region where water is abundant.
One implication is that he becomes much more powerful. The Rinnegan gives him access to powerful abilities like the Six Paths techniques, which would change the power dynamics in battles in the fanfiction. He could now face stronger enemies more easily.
One possibility is that there's some ancient chakra or energy in Wave that interacts with Naruto's own chakra. The unique environment of Wave, with its water and nature elements, might have caused his Mokuton to awaken. Another reason could be that Naruto has some kind of connection to the First Hokage that gets revealed during the Wave mission, and that connection enables the Mokuton awakening.
When Naruto awakens Mokuton in the Wave fanfiction, his role in the Wave mission is transformed. Mokuton is a powerful and versatile ability. Naruto could use it to camouflage the group by creating a forest - like environment, making it harder for the enemy to find them. He could also use wooden constructs to hold off attackers while the others carry out the main objective of the mission. This new power elevates his status from a novice ninja trying to prove himself to a crucial part of the mission's success.
Well, one way could be through some super - rare and powerful jutsu that transfers the dojutsu abilities to him. Maybe a forbidden jutsu that was long forgotten but he stumbles upon it somehow.
In some fanfictions, Naruto might obtain all dojutsu through some kind of ancient inheritance. Maybe he discovers a long - lost scroll or a hidden temple that bestows upon him these powerful eye techniques.
He could get a Dojutsu that allows him to manipulate time. This would be a very powerful ability as he could slow down or speed up time during battles. For instance, he could slow down time to dodge an enemy's attack and then speed it up to counterattack.