The HTML spec says that the <dialog> element is for:
part of an application that a user interacts with to perform a task, for example a dialog box, inspector, or window.
This could be something like a dialog that appears when you click to edit a profile picture on a website - you aren't taken away from that page, but you have entered into a new state in that page where only a small amount of content is relevant to what you're doing, and normally it's not even visible (though it is part of the HTML and always present, ready to be displayed at the right time)
This pattern is usually called a 'modal window' and there are many examples of that you can find online, and a ton of plugins for doing it. Now this is something built-in to HTML that we won't need plugins for (once browsers support it)