CiviMail is a mailing feature that interacts with your mail server much like the 'Email' action you mentioned. The main difference is design ability and ability to handle mass mailing campaigns to large groups of people.
Basically, if you are sending to more than 50 contacts at a time or you need to track email opens or clickthroughs - you should use CiviMail rather than the 'Email' action.
CiviCRM has good written documentation on CiviMail here: http://docs.civicrm.org/user/en/4.6/email/what-you-need-to-know/
(be sure to check out the other CiviMail sections around the linked section as well).
Edit: Bounce processing is another function that CiviMail is capable of. Processing bounces from your mailings is important to keep your sending reputation high in the eyes of other mail serves, to be sure your emails get through to people. This is especially important if you send using your own mail server and manage this yourself.
More info here: https://book.civicrm.org/user/current/advanced-configuration/email-system-configuration/
and here: https://wiki.civicrm.org/confluence/display/CRMDOC/Bounce+Handling