What is a broken link?
A broken link or dead link is a hyperlink on a web page that no longer works, and redirect the users that click on it to a 404 error page.
A link can be broken for different reasons:
There is a typing error in the URL (can be a space, an additional number of letter).
The destination page doesn't exist anymore.
The destination website of the link doesn't exist anymore.
The user has software or is behind a firewall that blocks access to the destination website.
Why you don't want to have broken links in your emails?
Broken links in emails are very deceptive for the recipients. As they will be redirected to an error page, they won't access the content you wanted to share with them.
Thus, emails having broken links inside are more likely to reported as spam by recipients. Which can have a strong negative impact on your email deliverability.
Some spam-filters are also tracking broken links and can directly place your email in spam if it contains such dead URLs.
The best practice is to always verify the links you send through emails, or to test your emails with tools like Warmbox "Email Spam Checker".