SO HAM = I AM THAT
At a very basic, physical level this reflects the sound of the breath. When used in meditation, such as Ajapa Japa, concentration on this mantra helps to align the consciousness with the breath. Physically this has the effect of regulating the nervous system, creating calm and relaxation.
On an energetic level, the sounds of sanskrit mantra align our being with paritcular qualities.
Sohamsohamsoham = I am that I am that I am...
"The word leads back to the sound: Sound creates a wave form, the wave form creates a word, and the word has an external meaning. By starting with the external meaning of the Soham mantra, the breath, we follow the word, so-hum, back through the wave form from which it came, and to the sound from which that wave sprung forth."
We create unity within by bridging the physical breath to the consciousness and expanding the consiousness.