Definition - What does So'ham mean?
So'ham, or So'hum, is a Hindu mantra that can be translated as "I am He/That." It is derived from the Sanskrit, Sah, meaning "He," and Aham, meaning "I." It is a universal and natural mantra because it is present within everybody as the breath, with the sound of "so" during inhalation and "ham" during exhalation. As such, So'ham is a mantra that is chanted just by concentrating on the breath because the breath chants it naturally.
There is also an inverted version of this mantra: hamsa, meaning "white swan," which stands for the inner Self.
Yogapedia explains So'ham
The So'ham mantra has been used for thousands of years to identify oneself with the Universal Reality. In Tantra and Kriya yoga, it is known as ajapa japa -- a constant awareness of the mantra, without chanting it. It is also believed that So'ham is an answer to Koham, meaning "Who am I?" The universe answers this question with So'ham, communicating that "You are the same as I am."
As a combination of Sah and Aham, So'ham also symbolizes the power of Shiva and Shakti, forming the male and female powers of the universe.