Imagine you have a website with the URL www.mywebsite.com
Now let`s say you want to add a blog to your site, with the URL of blog.mywebsite.com. That would be a sub-domain. If instead your blog URL is www.mywebsite.com/blog, it is not a sub-domain.
The best example I can think of is Yahoo. mail.yahoo.com and news.yahoo.com are sub-domains of the www.yahoo.com.