東 is often described as “the sun rising behind a tree”, but this is either a folk etymology or a reinterpretation of an already existing kanji.
東 originally represented a bag tied at both ends, and meant “bundle” (similar to 束, which maintains the meaning of “bundle”).
However, because it was a homophone (or near-homophone) of the word for “east”, and perhaps because “east” is difficult to draw, it was given this new meaning.
Continuing with the directions: 西