An internal link is a link between two pages of your own website: the menu, links in the text, breadcrumbs and references to related products. Google writes in its link guidelines that every page you care about should have a link from at least one other page on your site. A crawler finds pages partly by following links.
Why does it matter?
A page without internal links, an orphan page, is hard for search engines to find. Links in the body text to related pages also help readers and search engines see which topics belong together.
Example
Google generally only follows links that are an <a> element with an href:
<!-- Good: a real link -->
<a href="/dormers/planning-permission">Find out when you need planning permission</a>
<!-- Bad: no href, only a click action in JavaScript -->
<span onclick="go('/dormers/planning-permission')">Read more</span>Common mistake
Internal links only in a menu built with JavaScript, or with link text such as “click here”. Google recommends anchor text that is descriptive, concise and relevant.
How do you check it?
For each important page, look at which other pages link to it. During a website redesign this is a standard checkpoint; see Redesigning your website without losing search visibility.
More in the Technical SEO checklist.