Structure-wise, originally it was to mean an <article> would/could be like a mini-document or mini-page: a header, a footer, possibly asides and main content.
<section> was more broad, however due to sectionitis (a painful variant of divitis, and apologies to others medically educated for the horrid terminology) there's been some talk recently of stating something like, you shouldn't (or can't) make something a section unless the first bit of content in it is a header or heading (<h?> tag)... though someone brought up that ajax dynamically injecting content could make this a difficult hard rule.
But anyway that's something you could use as a rule of thumb... take what ralph said
An <article> is more specialized, being for self-contained content—that is, content that could appear somewhere else and retain its meaning.
and then use sparingly, and for sections ask yourself why it shouldn't be a div, and does it group a large chunk of content which starts with a <header> or heading <h?>? (even then, keep sections scarce and large, and use divs for all your little groupings you're doing for CSS, JS, etc).