One of my favorite parts of law school (please excuse this trip down memory lane) was taking writing classes. My school required two of them: Research and Writing (first year class), and Advanced Writing (usually a third year class). Research and Writing taught a research method and introduced the concept of "plain language." Advanced Writing made more targeted use of those skills through writing briefs, usually intended for an appellate case. (I also took another writing class, because I am a glutton for punishment, which I did as a directed study. Ask me if you ever want to see it, it's about the US Supreme Court's interpretation of the Americans with Disability Act, and other cases related to that).
The idea behind plain language is that a legal writer should make it easy for a reader to find the meaning in any document, and be able to understand what the writer is trying to convince the audience to do. This means using almost no "legalese," which might confuse the reader. Legalese would be something that sounds traditional and impressive, but actually makes its meaning more difficult to determine. For example, the phrase, "indemnify and hold harmless," where both terms could mean the same thing to a reader.
Brian Garner is often given credit for many of the plain language ideas. He's written books on the subject, and has (what I would think is) a dream job -- he edits other people's work to make it more reader-friendly, for use in legal briefs, and other documents. He is also cited as a source for
this government article on writing for your audience.
But - back to Novel Concepts in the Law: Plain language is a great way to win cases! Write for your audience, even if the audience is different from each other. The judge will know the law, go ahead and write a brief on what you're doing. But don't get all technical & weird in the writing. Make sure 1) your client understands why you're doing what you're doing, and it's good if they can understand your argument in the Brief and 2) the judge will have an easier time agreeing with you if you can make the writing easy for him or her. Just show that you know the law, too, and that it agrees with what you're trying to do for your client!