Broken links on a site and their impact on SEO
Broken links on a website are links that no longer work and result in an Error 404 response.
There are two reason why links become broken.
Internal broken links
These are links within the website which are no longer being found or return a 404 response. These can occur due to an incorrect or malformed URL, or because the page the link is leading to is broken or no longer exists. Multiple broken internal links may discourage users from visiting other pages of your website. Also, broken links prevent crawlers from indexing your site properly and as a result, your website ranking may be downgraded.
External broken links
Broken external links lead users from your website to another domain/website and land them onto a non-existent webpage. Multiple broken links negatively affect user experience and may affect your Search Engine rankings because crawlers may think that your website is poorly maintained.
Do they need to be fixed?
Yes, wherever and whenever possible. It is good SEO practice to monitor all the broken links on your site regularly. Google Search Console and Bing Webmaster Tools both report such links and there are various other tools available which report on broken links too.
Simply check the target URL. If it returns an error, remove the link leading to the error page or replace it with another resource/destination.