Well, there must be many reasons. However, I can think of one reason that can galvanize many motivations behind doing anything. I think, we love to experience things. Whether through our own life or through stories, movies, art, and expressions; we love to experience myriad of things.
We cook to experience a taste. We read to experience something real or imaginary that has been expressed by someone else. We watch movies, emotionally involved, to get a feel of many experiences that we cannot directly go through. We write, create, or express ourselves so that others can relate to us and enjoy our experiences. We dance, sing, entertain, cry, and do many things that will not only enrich us but will cater to others' desire to experience things.
I write, mostly in Nepali, and I am in the process of publishing my first book. However, I was wondering for a long time to know why would I want to publish? What can I contribute to the world that it already does not have? Then I realized that no matter how insignificant one may think, the experience I have gone through is unique in itself. So, if I publish a book with my expressions that reflect my unique perspective shaped by my one of a kind life experience, may be it will help others experience a story, creation, or life through my words. That I think would be pretty significant.
In a nutshell, I think it is the desire to experience a variety of things that drives us to play sports, go on adventures, read, write, watch, cook, create, act, dance,...whatever comes to mind.