How do Internal Links Affect SEO?
Internal links are critical to SEO success as the search engines use internal links to help discover new content. For example - unless you have an up-to-date sitemap, when you publish a new page on your website and don't link to it from anywhere else on your site, it will be invisible to the search engines because a crawler / bot won't know it even exists. Pages with no internal links are called orphan pages. You may well have some intentional orphan pages (for login pages etc) but it's worth checking to see if all pages you do want to be indexed in the search engines have inbound links.
Broken Links and How to Fix Them
Finding broken links on a small 5 page site can easily be done manually and won't take you long at all. Finding broken links on a large website with hundreds, or even thousands of pages, however, would be a very tough task if done manually. The good news is, there are many tools online that will find your broken links, often in a matter of seconds. Once you've done an audit on your internal links, the following relates to the type of broken links and how to fix them. Not just broken links, but also the quality of your internal links can be rectified here.
Broken Internal Links
Broken internal links are bad because you're effectively wasting some potential SEO (link equity / link juice) and they affect your user experience (UX or UE), which ultimately affects your SEO. Once you've identified your broken links, either reinstate them or redirect the broken links to another page, but only if it's relevant. If the page or content the broken link refers to no longer exists, remove all internal links to this content.
Internal Links to Redirected Pages
This is a link that is automatically being redirected to another page on your site. Please note, not all redirected links are bad (E.g. links redirecting from a non-secure http:// page to a secure https:// page), but it's still worth checking the pages that are being redirected as some can negatively impact your SEO. For example, if you 'used' to have a link that pointed to a sub-category called 'MacBook Pro', but this sub-category no longer exists and the link is being redirected to the parent category, which is 'PC and Mac' the actual link destination may not reflect the link anchor / call to action. Bad for SEO, bad for user experience.
Internal Links to Irrelevant and Unimportant Pages
The search engines are all about delivering accurate and high quality results, so it's important to make sure the content that the links on your website are directing them to is relevant and high quality. For example, if you have loads of internal links that are pointing to 'Christmas Sale' when it's almost Easter, these links are actually irrelevant and unimportant right now. Just remove them, and then reinstate them when they become relevant again.