Billie Joe Armstrong wrote that Green Day song about the woman he’d go on to marry. After the first kiss they shared he went home and wrote the song. It’s basically about being away from her.
Malakite/malachite is a green coloured mineral. For example: http://images.google.com.au/images?q=tbn:ZKfCz89OunXQUM:http://webexhibits.org/pigments/indiv/i/32mineral/malachite.jpg
Billie Joe has green coloured eyes. Therefore malakite in the song is referring to his green eyes. So when he says “She holds my malakite so tight so, never let go”, he means that he loves her so much that she’s the only girl he can see. If that isn’t brilliant song writing I don’t know what is!

