With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. (Editing for conventions should demonstrate command of Language standards 1-3 up to and including grade 8 here.)

This standard basically says that students should be going through some sort of planning and revision process. Because others can spot mistakes much more easily than writers themselves, don't count out those peers and adults.

Also, did you find the "how well purpose and audience have been addressed" line confusing? (We certainly were at first.) Well, don't worry—we've got you covered. The Common Core just wants eighth graders to make sure their essays are clear. If it's a persuasive essay, the argument should be supported throughout the paper. If it's an informative essay, it should describe in-depth what's going on. And if it's a narrative, the paper should feel like a story rather than an essay. As for audience, make sure students recognize that different writing styles are needed based on who they're writing to (such as adults versus elementary school kids) or the kind of writing they're doing (such as narratives versus formal essays).