Katara became a very powerful waterbender. The Last Airbender notes that the Fire Nation had killed all of the airbenders (including the Avatar) and so they went looking for the next incarnation, a waterbender, next. Reddit user LDM123 suggests the Fire Nation constantly pillaged and imprisoned members of the Southern Water Tribe because they originally thought Katara was the new Avatar.
Now, an intriguing new theory offers a compelling explanation for the Fire Nation's fixation with waterbenders before and during Avatar: The Last Airbender. When Aang disappears for 100 years, most people assume he's gone for good and focus on dominating the Earth Kingdom and Water Tribes, while a select few ( Zuko) continue to seek him out the Avatar.
Fire Lord Sozin instigated the war and proceeded to find the new and reborn Avatar following the death of Avatar Roku. The opening sequence of Avatar: The Last Airbender begins with the history of the four nations - the Water Tribe, the Fire Nation, the Air Nomads, and the Earth Kingdom - living in harmony before the Fire Nation became hostile to its neighbors.