What is non-attachment?

As thoughts arise,
destroying them utterly without any residue in the very place of their origin is
non-attachment.

Just as the pearl-diver ties a stone to his waist, sinks to the bottom of the sea and
there takes the pearls,
so each one of us should be endowed with non-attachment, dive within
oneself and obtain the Self-Pearl.

~ Who Am I? (Nan Yar?)
The Teachings of Bhagavan Sri Ramana Maharshi