Article:
It represents a self-contained composition in a document, application, or site.
It could be a forum post, a magazine or newspaper article, a blog entry, a user-submitted comment, or any other independent item of content.
An article elements can containing sections elements.
Example:

<article>
  <header>
    <h1>What is Lorem Ipsum?</h1>
    <p>WWF's Lorem Ipsum:</p>
  </header>
  <p>Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s</p>
</article> 

Section:
It represents a generic section of a document or application.
A site could be split into sections for introduction, content, and contact information.
A section elements containing article elements.
Example:

<section>
  <h1>Lorem Ipsum</h1>
  <p>Lorem Ipsum is simply dummy text of the printing and typesetting industry.</p>
</section>