Avatar: The Last Airbender
Avatar: The Last Airbender was a TV show that first aired on Nickelodeon on February 21, 2005. Ten years later, it's pretty much a classic and has spawned a sequel series, comics, a diverse fanbase, and a movie.
Assuming you've already seen the series and would like a little review, I'll provide short summaries for both shows. In The Last Airbender, some humans are able to use telekinetic abilities to manipulate, or "bend" one of four elements: water, earth, fire, and air. The Avatar is a person who, put simply, is half spirit and can bend all four elements. He/she is meant to keep the peace between the four segregated countries, each named after the element its people can bend. The Earth Kingdom is the largest, the Fire Nation the most advanced, the Air Nomads are generally peaceful while the North and South Water Tribes are none of those.
100 years ago, when a comet made the firebenders ridiculously OP, the Avatar, airbender Aang, fled his temple/responsibilities and ended up freezing his pet air bison and himself underwater. Meanwhile, the Fire Nation systematically wiped out his entire race in one day. Firebenders continued to oppress the other two countries. 100 years later, Water Tribe siblings Katara and Sokka are whining at each other and accidentally crack open the ice ball around still-alive Aang. After he affirms his identity as the Avatar, the three go on to spend three seasons defeating the Fire Nation and its psychopathic royal family.
...I think I just paraphrased the entire opening sequence.
The Legend of Korra
The Legend of Korra was the direct sequel to The Last Airbender, first airing on April 14, 2012. It is much more controversial than its predecessor, dealing with numerous topics "too mature" for a children's show, but is nevertheless embraced by most fans as a worthy addition to the series. Nickelodeon has not treated the series well, pulling it off the air halfway through Season 3 and putting the rest online.
In the Legend of Korra, it has been 70 years since Aang defeated Fire Lord Ozai and brought peace to the world. In that time, he and Fire Lord Zuko created the United Republic of Nations, land taken from Fire Nation colonies in the Earth Kingdom, with Republic City as its capital. The world began going through an industrial revolution, enhanced by newly widespread sub-elements like metalbending and lightning.
Korra, the new Avatar in the cycle, was born into the Southern Water Tribe immediately after Aang's death at 66/166. After a close call with anarchist kidnappers as a toddler, Korra is sheltered for her entire childhood and learns to bend in a training complex, with Katara (it's the same Katara) as one of her teachers. Korra masters water, earth, and fire by 17, and to learn airbending, she decides to go to Republic City, where Aang's only airbending child, Tenzin, lives. She meets orphaned brothers Mako and Bolin through bending sports and Asami, daughter of a rich car company's owner. Unlike Aang, who faces the one big threat of the Fire Nation, Korra faces four very different kinds of enemies through her four seasons, and grows from a aggressive and pouty teenager into a capable Avatar.
