The $user API variable is your connection to the current user viewing the page.
Unless a user is logged in, $user is always referring to the guest user account. If the user is logged in, then $user can be the superuser or any other user that you may have added to the system.
Technically $user is just a Page object (like $page), except that it contains fields and methods specific to a user. See the full $user API reference for full details on the available methods and properties. Note that $user is represented by the template named user, which can be viewed in Setup > Templates, after adjusting the filters to show system templates.
Examples
Depending on the context, you may have to call $user->of(false);
to turn off output formatting before assigning values to a user.
Changing the user's password
<?php $user->pass = "Bam!"; $user->save();
Adding a new user with the "superuser" role
<?php $u = $users->add('gonzo'); $u->pass = "BamBam!"; $u->addRole("superuser"); $u->save();