Why is there a page in a CiviCRM WordPress install that says "Do not delete this page."
CiviCRM has some public-facing pages that it generates. e.g. event registrations, unsubscribe confirmations etc.

On Wordpress the page you're seeing is the one that's used by CiviCRM for these purposes. So it's not a page you use or link to directly yourself, but it has to exist as far as Wordpress is concerned so that CiviCRM can provide dynamic content.

EDIT

Here's an example of when CiviCRM will use this page. You have an event, you want to give people a link to sign up for it.

From the Manage Events page you click (1) event links, then you see (2) test and live event registration links. You right-click the one you want and choose "Copy Link Location" (or whatever similar description your browser offers), and send people the link.

When people click that link CiviCRM will use the base page to decorate its sign up form.