What can energybending do?
Not much is known about Energybending. Before the four elements and the avatar were created, Energybending was the only bending-art in the world. Out of this, the four bending-arts were created (Airbending, Waterbending, Earthbending and Firebending), so these are based on Energybending. Energybending is the base of all arts. While the for bending-arts are based on the Chi, Energybending works a little bit different: It bends the energy in general and not the Chi.

With that, Energybending can be used to take and restore bending-power and knowledge (nothing more is shown, but I guess that much more is possible):


Avatar Aang uses the ability to take bending-power from Ozai in the last episode of Avatar: The last Airbender. This is a dangerous technique, as the soul of the user must be completely clean; otherwise, it can happen that the victim takes over the user.
Both the lion turtle (in Avatar: The last Airbender) and Aangs Spirit (in The Legend of Korra) use Energybending to transfer knowledge to other people. I guess it's possible to take memories, too, but that's nowhere proven.
Korra uses the ability to restore bending-powers to help some victims of Amon. The spirit of Aang uses that ability to restore Korras powers.


Also, Energybending is the only bending-power that can be used by a spirit without a medium (as shown when Aangs spirit teaches Energybending to Korra).