The ability to express oneself in a written medium. Typically this involves imposing a structure on the expression (i.e. choosing between the novel, press release, short story, personal letter, business letter, encyclopedia and scientific article forms); developing a logical flow of argument and selecting appropriate language and terminology. All this in done with reference to the target audience and the message trying to be communicated.

Writing skills are somewhat culturally dependent, since both structures and vocabulary are entirely cultural artifacts.

I've been told that structures and vocabulary aren't entirely cultural artifacts. I believe they are: structures are a cultural artifact because in many oral-based cultures (for example the Maori in New Zealand) the oration is the only structure, while in English orations are not an acceptable mainstream structure; vocabulary is entirely a cultural artifact because there are mainly pairs of languages which have no vocabulary in common.
deep thought says "To be skilled at this practice is no more a cultural artifact than oil painting or violin playing." And I agree with him. The difference between us is that he sees neither writing skills, oil painting or violin playing as cultural artifacts and I see them all as cultural artifacts. No non-western culture features violin playing except by pollution (or cross-fertilization if you prefer) with western culture.