In it's Oracle form 自 is a pictograph of a nose, with the nostrils and bridge clearly depicted. The nose marks the center of the face, and is where we often point when indicating ourselves. Early Chinese people observed this behavior and created the character "自" accordingly.
The famous Chinese philosopher 老子 (Lǎo Zi) once said, "Knowing others is intelligence; knowing yourself is true wisdom. Mastering others is strength; mastering yourself is true power."
自 is used as a radical in words like: 息 (interest), 鼻 (nose).