Checkmk is using the locally installed mail transfer agent (MTA) for sending e-mails. See Notifications - via Email, SMS, Ticketsystems and more for details.
The Checkmk Appliance already ships with an MTA installed (nullmailer) which can be configured on the webconf interface. On other Linux systems, you need to set up an MTA for yourselves. This does not need to be a fully-featured daemon like Postfix oder Exim, a simple forwarder like Nullmailer or SSMTP is usually sufficient.
The ~/etc/mail.rc file is the configuration for the mail user agent (MUA) used by Checkmk for sending e-mails to the MTA.