Music is as integral to me as my own DNA. My life has become a continual soundtrack, with music underscoring the most powerful and even the most banal moments of my life.

This quote means that music is extremely important to the speaker and is a big part of their life. Music is fundamental to them, just like their DNA, and it is something that is always present in their life, providing the background to all of their experiences, from the important ones to the more mundane.