If you have moved URLs or have an incorrect link to your site, it will generally generate a 404 Not Found error to the browser. While you can also style this page to make it match the site, the end result is generally the same. If a user hits this link, either way, they won't find the content they were originally searching for.
With a small amount of trickery, we can instead turn the 404 into search parameters to push through to your site. This way, you can either match the page or item the user was looking for or at least display the best guesses for them.
While most modern CMSes either have this functionality built in or have a plugin to handle it for you, if you're stuck with an older system or custom coded site, then you can quickly add this functionality.