Explosion allows Katsuki to excrete sweat similar to nitroglycerin from his palms and ignite it at will to create various explosions.
Through either one of his palms, Katsuki creates fiery shock waves that are highly powerful and destructive, often burning and/or shattering whatever they hit, with Katsuki himself being (initially) immune to them save for some recoil. Because this Quirk generates light, it's a natural counter to Dark Shadow.
The more Katsuki sweats, the more powerful the explosions become. This essentially means that Katsuki gradually grows in power the more he fights, since he will naturally sweat more under ongoing physical activity. However, during cold weather, the nitroglycerin-like sweat requires a slightly longer time to detonate, as opposed to heat, where conditions are optimal for ignition.
Repeated explosions, particularly large ones, eventually result in throbbing pain to Katsuki's arms and shoulders. Additionally, creating explosions with both arms at the same time causes their overall strength to disperse between both limbs, leading to individually weaker blasts.
Katsuki is able to use Explosion to propel himself through mid-air, blind opponents, and release long-range blasts, among other applications. Explosion is a versatile Quirk, especially for battle situations, as the recoil caused by the blasts can be exploited by Katsuki for mobility purposes. When coupled with his fighting talent and intelligence, Katsuki can come up with new moves with little difficulty, even having a few ready by the time he started U.A's school year. Thanks to Katsuki's battle ingenuity and natural aggressiveness, Explosion tends to be a very overwhelming Quirk for others to face off against.
In battle, Katsuki prefers all-out offense, using his Quirk's propulsive abilities to close the distance between him and his opponents, followed by a bombardment of close-range attacks that are often started with a powerful right hook. Despite having great mastery over his Quirk, Katsuki tends to recklessly cause unnecessary damage to his surroundings, which is a common issue with hero work as it may jeopardize missions that require more careful approaches.
Katsuki is very proud of his Quirk. Throughout his life, people frequently commended Explosion, leading Katsuki to develop a superiority complex. As a result, he became arrogant and condescending over others and their Quirks. Before getting into U.A. High School, Katsuki had the habit of using Explosion as a means of threatening and bullying Izuku, and while he has dropped that practice for the most part in the present, he still likes to use his Quirk to intimidate foes during fights, usually by creating miniature explosions around both his palms.
As mentioned by Katsuki himself, the Grenadier Bracers from his costume serve to reduce the risk of physical strain caused by overusing his Quirk.  Those bracers store part of his explosive sweat, with Katsuki being capable of igniting all of it at once by triggering one of the bracers' firing pins, releasing a massive blast that, while devastating, tolls the shoulder of whoever uses it, although Katsuki seems to be completely unfazed by this due to his superior physical ability. Katsuki also carries around grenade-like containers that can be filled with his sweat, allowing him or someone else to use them as actual explosives.
Named Super Moves
- Blast Rush Turbo (
爆 速ターボ Bakusoku Tābo?): Katsuki throws his hands back and then causes an explosion in his palms, to propel himself forward. This move can also be used to achieve a pseudo form of flight, as Katsuki used this move to fly over the giant robots during the Obstacle Race during the Sports Festival.
- Stun Grenade (
閃光弾Sutan Gurenēdo?): Katsuki creates a sphere of light with his hands. The sphere of light implodes, causing an explosion around Katsuki, blinding anything in Katsuki's vicinity. 
- Howitzer Impact (
榴弾砲着弾Hauzā Inpakuto?): Katsuki dashes into the air and creates two Explosions in his hands. While in the air, Katsuki spins himself around, building up momentum for his Explosions. After spinning himself around and gathering momentum for his Explosions, Katsuki fires an Explosive tornado at his opponent.
- AP Shot (
徹甲弾Ei Pī Shotto?, literal meaning "Armor-Piercing Shot"): Katsuki stretches out one of his hands and uses his other hand to form a circle on the palm of his outstretched hand. Katsuki then fires an explosion through the circle, which creates a concentrated blast beam. By focusing his the path of his explosions into a single point instead of around his whole palm, Katsuki creates a concentrated blast with reduced area of impact, but with enough power to successfully pierce even solid concrete.
- Explosion - Wikipedia article about the phenomenon Katsuki can create with his Quirk.
- Nitroglycerin - Wikipedia article about the substance Katsuki produces from his hands.