If you enable this module, the "From" address on contact emails, both site emails via the contact form and user-to-user emails via the member contact form, will be "From" the email address configured in site_mail (admin/config/system/site-information in d7). The reply-to header will be set to the address that Drupal would have used as the From address.
Note that Drupal 8 has this feature in core, so this module is not needed in D8.
This avoids many spam-classification issues. Many, many mail handlers will classify as spam a mail that comes from an unauthorized location, as this is spoofing. What Drupal does by default is spoofing...
Dreamhost actually *prevents* the sending of Drupal emails in many cases. This module should resolve that problem, but it's a problem elsewhere almost everywhere the Drupal contact form is used.
If you don't mind using a 3rd party service and have a nontrivial site, you'll probably enjoy the mandrill module and service. If you're on Dreamhost shared hosting, though, it probably means you have a trivial site to maintain and Mandrill would be overkill and additional complexity.