"Writing is not just a process of creation. It is also a process of self-discovery." —Cristina Istrati
“How can I know what I think until I see what I say?” —E. M. Forster
With most writing tasks, you are of course writing for a particular audience, whether it be your professor, advisor or thesis committee, your boss, perhaps a client, even the public. And thus it is naturally important that your tone, style, and format be appropriate to that audience.
In expository or argumentative writing, however, you are also, if you approach the task correctly, writing for YOURSELF. Think about why you are asked to write papers about such things as history, literature, or other humanistic subjects. To show that you have learned the material the professor wants you to, yes. But it’s more than that. We also assign you papers to help you to learn to think critically. Good writing is good thinking, on paper (or computer).
The world is complex. Social and political issues are complex and we as human beings are complex. Ideas and thoughts are slippery. Getting them down on paper and working through them—creating a cogent, logical argument with adequate evidence—not only engages you in the material but helps you explore an issue and discover or work out what you think about it. (Those of you who keep a journal and use it to work out personal problems already know this process well.) As novelist F. Scott Fitzgerald (The Great Gatsby) noted, “The test of a first rate intelligence is the ability to hold two opposed ideas in the mind at the same time and still retain the ability to function.” And writing those ideas down can help you work through them to figure out how to move forward.
Another way to look at it, as long-time college writing instructor James Slevin has put it, is the difference between “having a point” and “making a point.” The former is just saying what you already think you believe without analyzing it, while the latter is building an argument, collecting and weighing the evidence on all sides and possibly even switching your position as you write!
Writing, in other words, is thinking, learning, and discovery. And thus a good writing process moves with the following trajectory:
Writer-oriented -------------> Reader-oriented
 Fitzgerald, F. Scott, “The Crack-Up.” Esquire, February 1936.
 Slevin, James, “A Letter to Maggie.” Teaching Composition: Background Readings. 3rd ed., Bedford/St. Martin's, 2008), pp. 59-64.
"Bright idea" graphic by LeoRomero (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons