A 404 error page can be a static or a dynamic page depending on the type of website you have, It is the page that shows the “page not found” error message if a page has been deleted or removed.
It is recommended that you provide the search engines, robots etc with a 404 page to help them index the site completely. If you have a content managed site then this facility should be taken care of automatically.
Hint: Why not put a sitemap on your 404 page to help indexing!