If writing is illegible, you cannot read it, or you can read it only with great pain. The letters may be too small, too faint, too rushed, or piled on top of each other. A doctor's handwriting is the classic joke, but a wet stain, a bad photocopy, or a name scribbled in a hurry can all be illegible. Though actually, this word is only about the look of the marks. A page of simple English can be illegible; a page of hard English in clear print is not. It is a normal, slightly formal adjective, used by teachers, clerks, and anyone who has to read other people's notes. It is not slang, and it is not about the law.