So imagine you've moved a few pages around or renamed them to improve your SEO maybe. But what if when you first created those pages, someone was kind enough to link to them, without you even being aware of it most likely?
If someone follows that link on another site to your page then they are going to get a 404 Page Not Found condition and end up on your Page Not Found page. Annoying for them because they probably saved a link to your site thinking that that would be useful information to help them in future. And all this happens without you knowing about it!
Finding broken incoming links
Finding broken links going out is easy. You could just go to each page, spot the links and test them. Laborious but for most people with a smaller site, probably the easiest way. But incoming broken links is a different scenario. What do you do when you don't even know you have a problem?
You need an external service that monitors website links between different sites and spots that some of them are no longer valid. That service has to keep a massive amount of data to do that as there are millions of sites that could be linking to yours.