Swami Vivekananda on the True Meaning of Non-attachment

The man who gives up living in houses, wearing fine clothes, and eating good food, and goes into the desert, may be a most attached person. His only possession, his own body, may become everything to him; and as he lives he will be simply struggling for the sake of his body.
Nonattachment does not mean anything that we may do in relation to our external body; it is all in the mind. The binding link of ‘I and mine’ is in the mind. If we have not this link with the body and with the things of the senses, we are nonattached, wherever and whatever we may be.
A man may be on a throne and perfectly nonattached; another man may be in rags and still very much attached.
Swami Vivekananda