Fire Bending: Korra can control and manipulate fire by channeling chi through it. Fire bending is very straight forward and can do little more than cause harm, but it is readily available everywhere as channeling chi into the air can cause it ignite hence Korra can use fire nearly everywhere.
Water Bending: Channeling chi into water allows Korra to control this very versatile element. Korra can turn it to ice or steam at will and can it even has the advantage that she can use it to heal wounds. The downside of this element is that Korra needs a source of water for it to work. Although she can concentrate enough power that she can make water from air particles, the result is at best a few droplets.
Earth Bending: Rock, gems and crystals, all can have chi channeled through them to be controlled by Korra. Although Korra's mastery over this form of bending is great, she does not yet have access to some of the more complex forms such as metal bending or tremor sense.
Air Bending: The type of bending that took the longer for Korra to master. This bending is by far Korra's weakest but she is still able to use it to great efficiency. She can create great currents of air and even use the wind around her to grant her limited flight.
Spirit Bending: In its simplest forms, chi bending is the control of chi itself. Korra can use this to sooth frenzied spirits and calm them, though she is still learning how to properly control it.
Up Close and Personal: Even without her bending and her Avatar state, Korra is an extraordinary martial artist. She is in peak physical condition and has the level of endurance, agility and strength of an Olympian athlete.
Naga: Where Korra goes her Polar Bear Dog also goes with her. Naga has followed Korra even into this Twisted land.
Broken Link: All of the Avatars before Korra were formerly able to contact their past selves and ask for advice. However, after Korra's confrontation with the Dark Avatar she has lost this link seemingly permanently, and no longer has access to any of her past lives.
Korra comes from a world where humans are in touch with their inner chi to a level where they can control the elements around them. These people are called benders and are divided into four categories, wind, earth, fire and water. These are all divided in four categories as well, the Fire Nation populated by fire benders, the Earth Kingdom populated by earth benders, the Northern and Southern Water Tribes populated by water benders and the Air Nomads.
To ensure balance and order in this world and to prevent any one country becoming too powerful and wiping out the other, from the beginning of time when humanity acquired the ability to bend the elements, there has been a single individual tasked with enforcing peace amongst all. The Avatar, he who has control over all four elements.
Though mortal, when the Avatar's life comes to an end he will be reborn into a new body via reincarnation, thus ensuring that the cycle continues and the elements are preserved.
Korra is the latest Avatar in this cycle, born after Avatar Aang who stopped the 100 year war. She has big shoes to fill.
Korra's story begins where she was first discovered by the White Lotus society, an organization created to assist the Avatar and its future reincarnations. She was the daughter of the southern water tribe chieftain, and from very young she possessed the unique ability to bend the elements of water, fire and earth, a trait that decidedly marked her as the new Avatar.
Taken from her home, Korra threw herself with great eagerness at the task of being the Avatar. The girl had boundless conviction and she would train for the next 10 years to become the best fighter she could possibly be, mastering fire, water and earth at a very young age.
Despite her obvious talent and eagerness, Korra had been unable to bend wind for the longest time and thus the White Lotus society sent her to train with the last known air master, Tenzin, son of the late Avatar Aang. He resided in Republic City, a place where people from all over the countries lived independently.
Korra had a lot of trouble getting the hang of air bending. There was an unquenchable fire inside of her that prevented her the peace required to conquer air. It was not until a group known as the Equalists terrorized the city and ultimately stole Korra's bending abilities that she was able to learn air bending out of desperation and was able to defeat Equalist leader, Amon.
Through her adventures in Republic City, she met her close acquaintances, Bolin, Asami and Mako, who helped her in her quest and would remain close friends
After the events of the Equalist revolution, Korra had not only developed Air bending but Energy bending as well. Not a very powerful sort of bending per se, but very versatile as it deals with the internal spirit of the body and the outward spirit of the natural flowing chi of the planet. It was through this bending that Korra was able to restore the bending abilities from the people that Amon had chi blocked.
It was also through this energy bending that Korra caught the attention of her uncle Unalaq, the Northern Water Tribe chieftain. Under the pretense of becoming her spiritual adviser, Unalaq planned to steal Korra's power for himself and become the Dark Avatar, a creature that directly opposed the Avatar by striving to cause cause in the world.
Although Korra and her friends were ultimately able to defeat him, the cost was great and Korra lost all contact she had with her past lives. However, she did manage to re-open the path to the spirit realm and bring balance once more to the planet by returning air bending to the world. Previously, almost all air nomads had been annihilated thanks to the 100 year war with the Fire Nation and Korra managed to bring them back from the brink of extinction.
More would happen to Korra as she returned to Republic City, but it's in this particular time of her story that she'd find herself drawn to Twisted.