usually writing is associated with communicating with others. There is always supposed to be an audience for the text. But sometimes that audience can be just yourself.
I've already written about how writing can be a tool for thinking. Putting those thoughts into actual words can gibe them new perspective and concrete meanings.
Writing can also be a tool for learning. Being able to write about something requires certain amount of knowledge about the subject. And it's also great way to make you remember the things better.
Writing things down to remember doesn't always need to mean learning either. It can be simply remainders as well.
It can also be used to express feelings. Just like with thoughts, putting your feelings in words can help you process them.
And of course it can be used to learn to write better. When you are still unsure to show your writings to others. But I would still suggest getting feedback as soon as possible. It's the best way to improve in any skill.