In the animated series "Avatar: The Last Airbender," Fire Lord Sozin orchestrated the genocide of the Air Nomads primarily because they stood in the way of his ambition to spread the Fire Nation's influence across the world, and because destroying them was the only way to guarantee the Avatar cycle could never produce an airbending Avatar to stop him.
According to the show's backstory (fleshed out further in the comics and the prequel novel "The Rise of Kyoshi" as well as flashbacks in the series), Sozin became convinced that the Fire Nation's prosperity and technology gave it a duty — as he saw it — to "share" its way of life with the rest of the world, by force if necessary. His closest friend, Avatar Roku, opposed this imperial vision and warned Sozin against it. After Roku died (partly because Sozin withheld help during a volcanic eruption), Sozin realized the next Avatar would be reincarnated as an airbender, since the Avatar cycle moves through the four nations in order (Fire, Air, Water, Earth). An airbender Avatar, raised among the pacifist, spiritually attuned Air Nomads, would almost certainly oppose his plans, just as Roku had.
To eliminate that threat, Sozin planned and executed a coordinated, sudden attack on all four Air Temples during Sozen's Comet, when firebenders' power was massively amplified. The strike was intended to be total, killing every airbender, including children, so that no new Avatar could ever be trained in that element and no airbending lineage would survive to challenge him. The only survivor was Aang, the young Avatar, who escaped because he had run away from the temple shortly before the attack.
This act — often called the Air Nomad Genocide within the show's fictional history — set in motion the century-long Hundred Year War that forms the central conflict of the series, and it remains one of the darkest, most consequential events in the show's mythology.