Writing is a tool which has the function of expressing thought. It is a vehicle for thought.
As humans, we have the need of communicating our ideas to others. We are social beings, it is in our nature.
Vigotsky said that writing is a instrument of semiotic mediation, acquired in most cases in an educational institution, that at the same time enables us to internalize others of its kind. This is why writing is said to have a double function, as well as reading. It is part of the Advanced Superior Psychological Processes, and only humans are capable of acquiring it.
Western philosophers in the ancient Greece began to express their ideas and concepts through the written language and that, at the same time, influenced other philosophers and thinkers years and years after them. To have a clear proof (ideologically speaking) of the development of Mankind, the base for every single achievement of the species has probably been written somewhere (even if it is not in a common or average style).
The purpose of writing can be varied, as we can write to create a work of art, to inform of a scientific discovery, to express our feelings in a catarctic event, to share any kind of knowledge, etc.
I personally believe writing is a must because without the ability of doing so, leaving aside all the physical and mental advantages it rewards us with, we would be unable to share our own "self" with the universal self we are all part of.
Writers, on the other hand, are very important for the world because they carry the gift of being the voice of those who sometimes cannot have a voice, those to whom fate has not been kind, those who seek for a remedy to ease a mental pain. But also of those who enjoy a pleasant and quiet life, those who want to share a possitive message.
Moreover, writers are the influence of those who have not yet started their adventure,those who feel they want to be part of the great poem that life is, and want to contribute with a verse.