Dabi is one of the main villains in the world of My Hero Academia and he was introduced quite early into the series as a part of the League of Villains. As the story went on, his importance grew as well and, over the years, he's become exceptionally important to his own plotline that ties to some important Heroes. Dabi is central to the plotline of My Hero Academia which focuses on the Todoroki Family.
This is because he is actually a part of this family and this was revealed to the fans rather recently, in the Paranormal Liberation War arc. Dabi was given birth to with the idea that he would go on to surpass All Might and awaken the Quirks of both Endeavor and Rei. Eventually, he was branded a failure and he ended up being consumed by his own powers. Now, his hidden powers, which pertain to Ice, have finally awakened.
Dabi's Past
Dabi is the son of Endeavor and Rei and, just like his older siblings, was born with the idea of surpassing All Might in the future. Endeavor was obsessed with the idea of creating the perfect child that could do what he couldn't and, for that reason, he went as far as getting into a Quirk Marriage, where the sole reason for a marriage is to give birth to a powerful Quirk. Naturally, Endeavor wanted a child with both his and Rei's power and, in his opinion, this child could surpass even All Might. However, he kept failing in trying to create the perfect child. Dabi, just like his older siblings, was deemed to be imperfect, even though he had quite a lot of potential.
Endeavor looked his way and Dabi started training alone in an attempt to get stronger and impress his father. In fact, he awakened flames that were much stronger than Endeavor's own but the fact that he did not have Rei's ice powers meant that he was deemed a failure. Eventually, Dabi was told to not use his powers because he kept hurting himself and, more importantly, Endeavor was already busy with Shoto at that point. However, feeling neglected and wanting to prove himself, Dabi accidentally set himself on fire and was consumed by his very own flames.
Dabi As A Member Of The League Of Villains
Following this tragic accident, Dabi survived, thanks to help from All For One and Dr. Kyudai Garaki. Fans didn't get to see much of him from this point onwards, however, the abuse that he suffered, along with the fact that his father still continued the abuse with Shoto broke him. He chose to be reborn as Dabi and, at some point in his life, he ended up joining the League of Villains. His journey as a member of the League of Villains was illustrated throughout My Hero Academia and Horikoshi immediately established a revenge arc around him. It goes without saying that Dabi is an incredible character and, even though his character is meant to burn in the quest to take down his family, especially his father, it is still written amazingly.
The Paranormal Liberation War arc saw Dabi reveal his true identity to the entire world, along with the mistreatment that Endeavor threw his way when he was a kid. This only bled into the following arcs and the Final War arc of My Hero Academia saw him go head to head against his family. He ended up fighting Shoto, who Endeavor believed to be the genius and the perfect child of the Todoroki Family, and even defeated him in combat. Later on, he took on Endeavor himself and, in this fight, he decided to settle things and self-destruct.
Dabi's Ice Quirk
Shortly after it was revealed that Dabi is going to self-destruct, fans got to see a glimpse of his fight with Endeavor. While attempting to get him to put his flames out, Endeavor realized that something had awakened within Dabi. Quirks are very complex powers in the world of My Hero Academia and, sometimes, they can be pushed beyond all their limits and this is what fans know as Awakening. However, in extremely rare cases, especially when a power user experiences a near-death situation, their Quirk enters the state known as hysterical strength. This isn't like Awakening and can only bloom when a person is about to die. This hysterical strength awakened within Dabi and caused his Ice Quirk to finally awaken.
This Ice Quirk didn't come out of nowhere. Dabi's mother, Rei, possesses the power to manipulate ice. This ability was latent within him and finally decided to show itself in the Final War arc. Dabi now possesses the power to manipulate both fire as well as ice, just like Shoto. This is ironic as not only did Endeavor always have his perfect child in front of his eyes that he neglected but he also decided to destroy his entire family over it. Now that Rei's Quirk has awakened within him, Dabi is certainly much stronger than he was before. His flames already burn hotter than Endeavor's own and with the Ice Quirk, he can cool himself down, if he wants to. He is certainly a step above Endeavor in terms of power, and possibly even his brother, Shoto. That said, he is on the verge of death right now and, by the way things are going, he could very well end up dying in the next few chapters. To save Toya from death, the Todoroki Family will have to combine their powers and prevent him from self-destructing, which looks like it is going to happen eventually.