U.A.'s Big Three represents the top hero candidates in all of Japan. Mirio Togata, Tamaki Amajiki, and Nejire Hado did not rank well in their previous U.A. Sports Festival, and their strange personalities leave a strong impression on most people.
However, each member of the trio possesses an extremely powerful and versatile Quirk and have worked hard to master them in order to become the three very best students at U.A. High. During their senior year, Nejire and Tamaki were the first to gain recognition throughout Japan. Mirio was the last of the three to be recognized as a top hero candidate, and thus the trio is known as the Big 3 of U.A. High School.
The Big 3 is first introduced to Class 1-A by Shota Aizawa following the second term orientation. They are brought in to explain the Hero Work-Studies that students participate in on their own merit. Mirio decides to teach Class 1-A through experience and fights almost the entire class by himself. Mirio dominates them and explains how the Hero Work-Studies helped him improve to become the best student at U.A. High.
The Big 3 are widely known as the strongest three hero students in all of Japan. Thanks to Hero Work-Studies, the three of them have seasoned their skills and mastered their powerful Quirks at a young age. They are considered to be above Pro Hero levels already and are destined to become Top Pro Heroes once they graduate.
Nejire has a very powerful, ranged-type Quirk with various applications. She has a good enough handle on it to where she can easily overpower top-tier villains on her own.
Tamaki has been stated to have potential exceeding the majority of Pro Heroes. His personality holds him back, but his Quirk's versatility and his practical application of its powers can't be denied. He is also capable of outclassing most villains he comes into contact with. His mentor, The BMI Hero: Fatgum, even said that he was more capable than anyone else attending the raid. This includes himself, his fellow friends in the Big Three and even Ryukyu ranked Number 9 at that point in time.
Mirio is extremely strong. Mirio used to struggle to control his Quirk and nearly gave up on becoming a hero. After training with Sir Nighteye, Mirio learned to master his Quirk and became the very best student at U.A. High School. He effortlessly overpowered Class 1-A, who are considered to be prodigal students by first-year standards, on par with Class 1-B. Mirio is even considered to be the top candidate for the No. 1 Hero Spot, implying that he's even more inspiring than Endeavor and Hawks, the current top two Heroes.