Writing forces me to articulate ideas that make intuitive sense in my head, so other people can follow along. The process of flushing out the details is like having a debate with myself. Explaining something for the first time is often more like a brainstorming session than a polished presentation. But, after writing about an idea, I'm surprised by how much easier it is to explain it crisply.
The process of connecting language and meaning often helps to evolve / develop underlying meaning. Because many concepts are hard to translate, we're forced to find rhetorical devices to hint at our intended underlying meaning. Thinking of analogies and examples that can hold up to multiple levels of scrutiny is deeply satisfying.
Use writing as a tool. By writing, you'll deepen your understanding and refine your ideas so that they're easier to explain.