A 404/error page can be one of the most important pages on a website, displaying a message to the user when the requested URL cannot be found. It's a great opportunity to show off a website's personality, whilst offering help to what could be a potentially confused user. A website without an error page is really not good and should have that rectified right away.
Before I get onto why it's such an important page, let's look at what the 404 means. The error code 404 is a standard response code returned by a server to indicate that a webpage was successfully requested by a web browser, but that it was unable to locate it, which is where the "not found" part comes in.
There can be a few reasons why you might find yourself on such a page. In some cases, it appears that the user has made a typo in the URL. In most cases, it's because the website owner has made a change - either it is updating or redirecting the link, deleting the page and not setting up redirects or some other error on their part. For someone browsing your website though, they want to and expect to see a 404 page appear when something like this has happened so that they have some form of explanation/apology. It doesn't have to be much, so long as it's at least brief and clear.
Why is this one of the most important pages on a website, though? Mistakes happen, whether it's the user making a typo or the site owner removing the page in a redesign. You don't want that user to then leave your site disappointed. A user landing on a 404 page is not the end of the world providing you can keep the user's attention long enough to point them back in the right direction, and that's the important part. The placement of images and hyperlinked text goes hand-in-hand with this. Link to the home page, include a search box or recommend using the site's search in the header/footer, include some links to the latest articles - you never know, one of them might grab their interest instead.
The idea that a user mis-spelling a word in the URL, or a dead link, leads to the user ending up on a 404 page is useless is simply incorrect. Looking good doesn't make a good error page (it can help in getting/keeping the user's attention though), a good error page will help users find what they want to find. They ended up there for a reason. Help them to find what they were on your site for.
There's no need to lose a visitor because of a simple mistake. Websites can live off user engagement, so you need to keep your visitors on your site instead of making them wonder where a page has gone that they had saved as a bookmark or found a link to elsewhere, and leaving your site to find that information elsewhere.