Well, Nagato's story probably focuses on his childhood in Amegakure. He witnessed so much death and destruction there. He might tell Naruto about how he met Yahiko and Konan, and how they dreamed of bringing peace to their village. But things went wrong, and his experiences made him believe that only through pain could the world understand true peace. Naruto, on the other hand, believes in a different kind of peace, one achieved through understanding and friendship. So, these differences in their beliefs could be an important part of what Nagato tells Naruto.
Maybe he sees something in Naruto that makes him want to share. Naruto has a strong belief in peace that might make Nagato feel like he should explain his own actions and past.
In these fanfics, Nagato may help Naruto on an ideological level. Nagato once believed in a very different way of achieving peace. By sharing his journey and how he came to realize the flaws in his thinking, he can guide Naruto in his pursuit of true peace. Nagato could also use his influence over the Akatsuki remnants to prevent them from causing more chaos, which in turn helps Naruto in his mission to protect the ninja world.
In some fanfictions, Naruto and Nagato might be related through their shared experiences with the ninja world. They both faced great tragedies. Naruto could be seen as a successor to Nagato's ideals in a way. Nagato once wanted peace through force, but Naruto shows that peace can be achieved through understanding and forgiveness.
It would change his abilities in multiple ways. Firstly, with the Rinnegan, Naruto could have better perception of the world around him, similar to how Nagato was able to sense things from afar. Secondly, he might be able to use the Animal Path to summon powerful creatures. This would give him more options in battle. Also, the Rinnegan could potentially allow Naruto to access some form of chakra absorption or manipulation that he didn't have before, further diversifying his power set.
One plot implication could be that Naruto becomes a target for more powerful enemies. Since the Rinnegan is such a powerful and coveted dojutsu, many villains might want to either steal it from him or kill him to prevent him from using it. Another aspect could be that Naruto has to learn to control the Rinnegan's powers, which could lead to some internal struggles as he tries to balance his existing powers with this new and extremely potent ability.
One possibility is that there was some sort of spiritual or chakra - based connection between Naruto and Nagato. Nagato, being the possessor of the Rinnegan, recognized Naruto's strong will and the fact that he was on a path to change the ninja world for the better. Through this connection, Nagato was able to transfer the power of the Rinnegan to Naruto. It could also be related to the nature of the Sage of Six Paths' power that was somehow involved in this transfer, as both Naruto and Nagato were related to the Sage in different ways.
In some fanfiction concepts, there could be a spiritual or mental connection established between Naruto and Nagato. Since Naruto has this unique ability to understand and connect with people on a deep level. Through this connection, Nagato might pass on the power of the Rinnegan to Naruto. It could be like a transfer of not just the physical power but also the knowledge and understanding that comes with the Rinnegan.
Maybe Nagato had a relationship with an Uzumaki woman before he became fully involved in the Akatsuki. This woman could have given birth to Naruto but for some reason, Naruto was separated from Nagato at a young age. It could be due to the chaos and danger that Nagato was getting into with his plans for the Akatsuki.
He could be more light - hearted. Instead of being burdened by his past immediately, he might start off with a more positive outlook. For instance, he could be curious about the new world around him and approach things with a sense of wonder.