As I wanted to know more about what the system of my Raspberry Pi was trying to tell me I had to set up a Mail Transfer Agent (MTA). I was using a MTA called postfix in its local only mode.

Installing postfix package

I first made sure I had the newest list of packages:

sudo apt-get update

sudo runs the command with super user rights (actually not sure if this is needed here)

apt-get update checks for the newest lists of packages

Then I installed the postfix package using this code:

sudo apt-get install postfix

sudo runs the command with super user rights (actually not sure if this is needed here)
apt-get install postfix installs the package postfix

Check this thread on how to uninstall packages: http://askubuntu.com/questions/187888/what-is-the-correct-way-to-completely-remove-an-application

Configure postfix package

The configuration procedure was run automatically and I chose local only as I just wanted to ensure to being able to read system messages.

As system mail name I just went with the default name that was already set.

In /etc/postfix/main.cf I made sure to have this:

myhostname = localhost
mydomain = localdomain
inet_interfaces = $myhostname, localhost
mydestination = $myhostname, localhost.$mydomain, localhost
mynetworks_style = host

and:

default_transport = error:outside mail is not deliverable

Furthermore I chose

home_mailbox = Maildir/

to store messages in the subdirectory Maildir of my home directory.

After

postfix upgrade-configuration

I got the first message that I had new mail and the path where it would be found (standard path should be /var/mail/[username]).

Resources I’ve been using to learn this

http://cafim.sssup.it/~giulio/other/Postfix_Setup_for_Local_Mail_Only.html

in German: https://www.thomas-krenn.com/de/wiki/Postfix_unter_Debian_einrichten

http://unix.stackexchange.com/questions/23277/where-does-postfix-store-email