404 errors happen when someone requests a page or file that doesn't exist - actually, it's more accurate to say the web server can't find the file.
They're actually very common on the web. And they're never a good thing.
If you visit a site, you probably want to read or view content on that site. You won't stay on the site if the content is missing. Serving 404 errors to your visitors is a good way to lose them.
It doesn't matter if it's your fault, their fault, or someone else's. Maybe they clicked on a broken link caused by a typing mistake on another website. Maybe they cut-and-pasted a URL wrong. Or possibly they made a spelling mistake when they typed a URL manually.
Maybe you changed the URL of an article to make it more appealing to the search engines.
Whatever the cause, the result is a disappointed reader. So fixing 404 errors is a usability issue. Patching them up will result in more useful traffic to your site, and for many sites, that means more revenue.