(My) body (is) my holding cell. Or, "Body: my holding cell." The character of Mr Hetfield's song considers his own body to be a prison. Not as lyrical, is it? :)

My body is my holding cell = my body is my prison. I am consumed with my own thoughts and cannot escape this existence, least of all my own body. A holding cell is where they put accused lawbreakers who have been arrested and are awaiting processing. It is on a temporary basis, until the prisoner either makes bale (pays an assurance to show up in court) or is imprisoned in a more long-term prison.

It doesn't make sense. LOL.

I think it means that the song-writer is looking at the body as a temporary, or short-term prison for the spirit or soul. Prison might be too strong of a word. A holding cell is to keep people for a short period of time. They are not necessarily criminals, but some authority does not want them to go away, at least not for a short while.