U.A.'s Big Three represents the top hero candidates in all of Japan. It is unknown how they were selected or when they were established. Mirio Togata, Tamaki Amajiki, and Nejire Hado did not rank well in their second-year U.A. Sports Festival and their strange personalities don't leave a strong impression on anyone.
However, the trio possesses extremely powerful Quirks and have worked hard to master them in order to become the three very best students at U.A. High.
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 is 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 level already and are destined to become Top Pro Heroes once they graduate.
Nejire Hado 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 Amajiki 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.
Mirio Togata is the strongest of the big three and there appears to be a wide margin of strength between him and the others. 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. He effortlessly overpowered all of Class 1-A, who are considered to be prodigal students by first-year standards. Mirio is even considered to be the top candidate for the No. 1 Hero Spot, implying that he's even more powerful than Endeavor and Hawks. 
- ↑ My Hero Academia Manga and Anime: Chapter 122 and Episode 62.
- ↑ 2.0 2.1 2.2 My Hero Academia Manga and Anime: Chapter 123 and Episode 63.