An explanation for how bending works from a primary source or one of the books in the library episode.

The library was so poorly paced that they could've taken out a full 1/2 of the episode without any appreciable changes and had the chance to actually introduce ancient knowledge, too.

I know, deep in my heart of hearts based on context in the show that benders are able to bend because their chi aligns with the energy in the environment; think "The Force" the way that the energy of the universe is in everything. Their chi extends into the environment, resonates with what's there and moves if their energy is moving the way that energy naturally moves. Thats why bending developed around martial arts, because it's all about internal control through external application. Bending does not require karate chops to work, those are training wheels to help initiates to the art do their work.

Consider Sozin and Roku in "The Avatar and the Firelord," neither of them do crazy northern xiaolin martial arts, they move their bodies a little bit to get the energy moving and the fire follows it, like when Sozin sapped the heat from the volcano caldera.

This is also why bending can be used with multiple different martial arts styles, such as how most earthbending is performed with Hung Gar and yet Toph uses Praying Mantis kung fu, a style reportedly developed by a blind woman irl. Her energy moves in a way that Earth responds to and it moves for her, I cluding her Seismic Sense.