WordPress.org

What is this update nag you mention?

In versions 2.5 and later of WordPress, your WordPress will alert you to the release of a newer version of WordPress via a yellow-background update notice at the top of every admin page. WordPress 2.5 and later reports "WordPress X.X is available! Please update now!" or "WordPress X.X is available! Please notify the site administrator."

Why would I want to remove the update nag about new releases of WordPress?

Maybe you know about the newer WordPress release (either from the nag, news, etc) and don't want to be constantly reminded by your current WordPress install (not everyone can or wants to upgrade to the newest version immediately). Also, you'd like to recover that much real estate on the page for something of more interest to you.

How will I know WordPress has been updated if the nag doesn't appear?

Within the context of your WordPress admin, the footer of your admin pages will reflect that status of your version of WordPress (be it current or out-of-date). And if you are tracking WordPress progress at all (i.e. blogs, forums, your WordPress dashboard) then you likely don't need to be made aware of new releases anyhow since you'll likely already know about them.