My daughter used to play teacher and explain her school lessons to an invisible audience while writing on her dry erase board. It was a way for her to integrate her school lessons from the day and understand them better.
It seems that we teach best what we need to learn, or that we like to explain what we need to understand, or that we learn better if we teach what we're trying to understand. Understanding is a process that solidifies through teaching or writing for example - hence the idea of homework, or writing papers in college.
I am currently reading the book Learning By Teaching, which is chock full of relevant quotes. Author Donald Murray writes "Why do writers write? ......most of all to discover what they have to say." Brilliant! He goes on to quote novelist E.M. Forster, who said "How do I know what I think until I see what I say?" and poet Cecil Day-Lewis, who concluded that "We do not write in order to be understood, we write in order to understand." All these quotes express how understanding unfolds and deepens through processes, such as writing or teaching.
Murray even takes this realization one step further when he says that, "...writing is an individual search for meaning in life." We writers discover the meaning of our own life through writing; writing for us is a process of self-realization in the same way that painting is a process of self-realization for an artist, or baking pastries is a process of self-realization for a pâtissier.
Life is a process, life is self-realization - through interaction with people and things. We each chose to live, to be life, through the lense of a particular medium - for the painter the medium is his art, for the writer it is her books. What is your medium?