The statement ‘tat tvam asi’ — ‘that thou art’ — occurs in the Chandogya Upanishad, said V.S. Karunakarachariar, and elaborated on its meaning. The Supreme One manifested as all that is around us - sentient and non-sentient. He has for His body the world, and also the individual jivatmas. Everything, including jivatmas, is His property. We should not think of the atma as belonging to us.
If everything came from Him, why are we not aware of this? Some examples will help one understand better. Honey is gathered from various flowers. Do the drops of honey know which flowers they came from? Water from the ocean evaporates, and then rain-bearing clouds give us rain, which replenishes the waters of the rivers. These rivers eventually merge into the sea. Are they aware that they owe their origin to the sea?
The atma does not perish. If we cut the branch of a tree, the tree does not die. Other branches come up. In the same way, the atma may be likened to a tree and the body to the branch. Just as one branch of a tree is replaced by another, so also when one body is lost, another takes its place. But the atma itself never dies.
If Sat is not perceivable, then how can it give rise to a huge universe? The answer is that if you look at the seeds of a banyan tree, you will notice how small they are. Yet they give rise to huge trees. In the same way, Sat gives rise to the world.
If Sat is all pervasive, why do we not see it? Add a pinch of salt to a glass of water. Taste the water. It is salty, but do you see the salt? In the same way, you may not see Sat, but it is ever present. How then do you sense this Sat? If you are lost in a forest, you will have to find your way out. You may not see the way easily, but the way is very much there.
A man in the last stages of his life does not respond even to the voice of his dear ones. He no longer cares about anything of this world.
So if you realise that you need nothing but Him, then your relatives will no longer matter to you. Therefore surrender yourself to Him.