The deeper meaning of this Mahavakyam or great saying (of which there are 4 main ones) would run something like this imho ….
In Zen, one would say….
Each of us is more than the body, more than the mind. We are not the body, we are not the mind. What are we then?
If you look into the mirror, who or what is that looking back at you? That’s who we are in reality. Consciousness. Without it, we won’t be.
In Vedanta, one would say….
We are the tiny wave that is part of the ocean; we are the ocean. Big or small, we are still the ocean. It is just ocean.
A jewel droplet on the net of Indra. We are all connected. We are one.
As both my Zen and Vedanta teachers would say….
Sit, meditate, so that you can come face to face with the one who sees, you the see-r, the silent-witness, the immortal-one, the one-who-knows, the one-untouched, the ever-blissful-one-no-matter-if-the-sky-fell-down (unlike Chicken Little).
Related post: The story of Chicken Little – respond or react.