Berbs is trying to say that we go through stages in life, and that those stages are new chapters in our lives. We bring to new chapters what we learn from old chapters. This is comparable to reincarnation in the sense that you begin afresh from time to time.
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An Atheist friend of mind has a very scientific interpretation of reincarnation. He says that a person 'lives on' because he becomes one with the earth after being buried in it. You become one with the soil, which is used to grow food, which is eaten - and you are reborn.
Something like that. He explained it better and more eloquently.
Stardust to stardust, it's what we are made of and where we are all headed. In that sense, there can be said to be "reincarnation" in a grand, cosmological sense.
On a more human level, there's something about reincarnating within one's life, like what Berbs is saying, recreating yourself, perhaps not in the sense that some Hindus believe (as in your "soul" is transported into another body) but renovating your beliefs, changing, remembering how things were before those changes, so you can still relate to others, but continuing to grow, evolve, change, within your lifetime.