Maybe it's some kind of ancient bloodline that was dormant in his family for generations. It suddenly became active in him.
It could be a result of some kind of prophecy. The powers were bestowed upon him before birth to fulfill a great destiny. Or perhaps it was a side - effect of the Nine - Tails' chakra mixing with some other unknown energy within him during his gestation.
Well, his super powers might make him a target at first. People could be either jealous or scared of him. So he might have a hard time making friends. He'd also probably attract the wrong kind of attention from some villains who want to use his powers for their own evil plans.
He could have the power of energy absorption. So, when an enemy attacks him with a jutsu, he can absorb the energy and use it to strengthen his own attacks. It would be like a reverse - engineering of the attacks against him.
Well, Naruto's transformation into a Super Saiyan would likely bring a whole new level of energy manipulation. The Super Saiyan form is known for its intense ki energy, and Naruto's chakra could blend with it in interesting ways. His stamina would probably increase, enabling him to fight for longer periods without getting tired. His ability to sense danger and opponents might also be heightened, similar to how Saiyans can sense ki. And his overall presence on the battlefield would be much more intimidating.
Often, Orochimaru remains an antagonist even in these fanfictions. His thirst for power and immortality makes him a natural foe for Naruto, especially when Naruto has new super powers to protect. Another common one could be Madara Uchiha, as his grand plans for the world are likely to clash with Naruto's newfound abilities and his desire to protect peace.
Some fanfictions have Naruto getting super powers as a result of a divine intervention. Maybe the gods or goddesses of the Naruto universe see his great potential and decide to give him additional powers to help him in his quest to bring peace. This can lead to all sorts of interesting plot developments, like him having to prove himself worthy of these powers to the divine beings or facing the envy of other ninjas who don't have such divine blessings.
One interesting plotline could be Naruto having the power to control time. He could use this to prevent tragedies in the past, like the death of his parents. Another could be him having the ability to communicate with all animals, leading to new alliances and strategies in battles.
One possible power could be instant teleportation within a certain range. Some sage - like abilities in Naruto involve quick movement between spaces. Naruto, as a born sage, could use this to surprise his enemies in battle. He could suddenly appear behind an opponent or quickly move to a strategic location, giving him an edge in combat.
One super power often seen in such fanfiction is elemental manipulation. A character could have the power to control all four elements - fire, water, earth, and air - with great precision. They might be able to create huge firestorms to fend off dark wizards or summon tsunamis within the Hogwarts lake. There are also super strength powers where a wizard or witch can lift extremely heavy objects, like the entire Hogwarts castle, which comes in handy during battles against powerful dark forces. And of course, there's the power of invisibility without the need for an invisibility cloak, which gives a character an edge in spying or sneaking around.
His hidden powers might be the ability to control all five basic nature types without any training. In the original story, Naruto had to work hard to master different nature types. But in a fanfiction, it could be that he has this innate ability which was hidden all along. This would make him extremely powerful and feared by his enemies.
One interesting 'Naruto gets super powers' fanfiction could be where he gains the power to control time. This would completely change the dynamics of his battles and how he interacts with his friends and foes. He could go back in time to prevent tragedies or leap forward to gain knowledge of future threats.