The mantra So Ham has two sounds – “so” and “ham” which correspond to the Sanskrit words “sah” (that) and “aham” (I). Joining these together creates the Mantra “So Ham” which means I AM THAT. As per the Vedic texts (specifically in the Upanishads), here “I” means “individual soul” or atma and “that” refers to Paramatma or “High Consciousness”. So in short, the So Ham mantra means that I am the same as Universal Consciousness or in other words the individual soul or atma is a part of Paramatma and therefore the same as Higher Consciousness.
According to the Upanishads, recitation of this mantra has a meditative like effect as “So” is voiced on every inhalation and “Ham” with every exhalation. Here we are including both breath and sound as part of the meditation practice.