There is no "module", at least not one that can be turned on and off like other modules. Emails are normally handled by drupal_mail() and a bunch of other functions found in the
system.mail.inc file under /modules/system and
mail.inc found in /includes . These work together to create the framework, using templates that you can set up in order for other modules (like VBO) to actually send emails.
Sending an e-mail works with defining an e-mail template (subject,
text and possibly e-mail headers) and the replacement values to use in
the appropriate places in the template. Processed e-mail templates are
requested from hook_mail() from the module sending the e-mail. Any
module can modify the composed e-mail message array using
hook_mail_alter(). Finally drupal_mail_system()->mail() sends the
e-mail, which can be reused if the exact same composed e-mail is to be
sent to multiple recipients.