Ultimately, I think the quote means that the first link on a memorable day will blossom into your actions and shape and define you as a person. Therefore, I think the so called link refers to an experience we have as a child that will permanently define us in some sort.
Hmm. A memorable day in my life. I would say a memorable moment in my life was when I took my first baton lesson in 4th grade. I was extremely eager to twirl the shiny baton, and I remember coming home and showing my mom all the cool things I learned to do (and now when I look back I cringe at how bad I was when I started) I've realized how a simple hobby can develop into a passion and how sports and a strong work ethic can really shape your life.