At the start of The Last Airbender, we knew that Sokka and Katara didn't have much family. Their fates though were unknown at first. Their father was later revealed to be leading a war effort with the other men of his tribe. But their mother seemed to have suffered a terrible fate.
Finally, near the end of season 04, we found out the terrible truth. During their childhoods, the Fire Nation went to the South Pole (which was the weaker of the two Water Tribe clans) and take any and all Waterbenders there to ensure no resistance members there. Eventually though, they received orders to simply kill them.
Eventually, Katara's Waterbending powers began to arise, and somehow the Fire Nation found out about it. Kya hid Katara and confronted one of the soldiers, claiming she was the Waterbending they were searching for. She was killed after stating that.
Katara would spend most of her life afterwards wanting to avenge her mother, and she did find the one who did the deed. But she let him be, because she knew it wasn't what her mother would've wanted from her.
When her and Aang had a daughter, they named her Kya after her mother. Ironically, Kya became one of the best Waterbenders in the world in her time.