This functionality has nothing to do with Wordpress SEO: it can be done with or without the plugin.
To link to in-page content, you just need to add a #someword to your link (href attribute) and id="someword" to some tag surrounding the place where you want the link to lead to. I'll sometimes use <span> tags around anchored links.
Example:
<a href="#internallink">Internal linking</a>
<span id="internallink">internal linking part</span> you want to link to.You could also put the id=word variable in another href tag, a heading tag, paragraph or whatever. The place where you're creating the link needs the pound sign, but the place being linked to, after the id= part, doesn't. So long as the words match, you can use whatever you want in place of the someword / internallink examples.