“Shivoham” means “I am Shiva”. Shiva is the pure unbounded all-pervading consciousness (the transcendental self, the Absolute). Here is an explanation of “Shivoham” bhajan.
”Shiva” here means that innocent, blissful, splendid, golden, beautiful.
“Shivoham” — I am Shiva. Splendid, the most innocent.
“Shiva Swarupoham” — my nature is Shiva. My form is Shiva. I am made up of a substance that is Shiva — innermost me.
“Nityoham” — I am ever present. I am always there. Body dies, disappears, but I am there.
“Nityoham Shuddhoham” — I am ever pure. Nothing can touch me. All these things come and go, but they cannot touch me, they cannot do anything to me.
“Buddhoham” — I am always enlightened.
“Shivoham Shivoham Shiva Swarupoham. Nityoham” — I am eternal. There is no end to me.
“Advaita Ananda Rupam Arupam. Shivoham Shivoham Shiva Swarupoham” — There is no two. It is me in all the forms, all over. It is me. My breath is flowing everywhere. I am the formless though I am inside a form. My spirit has no form. Though I am formless, I move in forms, in all forms in the whole world.
“Brahmoham Brahmoham Brahma Swarupoham” — I am the Brahman, the totality, the all.
“Chidoham Chidoham” — I am the consciousness. I am lively. I am full of life. I am pure energy and pure consciousness.”
~~ Sri Sri Ravi Shankar