It's likely to be in the spool file:
/var/spool/mail/$USER are the most common locations on Linux and BSD.
Other locations are possible – check if
$MAIL is set – but by default, the system only informs you about
Usually the spool file is in a very simple mbox format, so you can open it in a text editor or pager. For a slightly more convenient way, most distributions come with a program called
mailx). You can try
mutt or (re-)
alpine; you can even configure it to be sent to an outside mailbox. (See "is this real mail?" below.)
- What does it contain?
- Who/What sent it?
Read it and find out :) Most often the messages contain output of cron jobs, or a system security report by logwatch, or similar junk.
Depends greatly on the contents of each message.
You should at least scan the subject headers – often people ignore the mail for months never realizing that their daily cron jobs fail.
Is this even actual "mail" in the same sense as email? Or is it just my system telling me something?
Yes, it's generated by your system telling you something. And yes, it's actual email, and can be handled as such.
You can (and often should) configure your mail software (the "MTA" aka "sendmail") to forward the messages to your personal address – the exact instructions vary depending on which MTA (if any) you have installed, whether this is a personal computer or a server, whether you have your own domain or use a @gmail.com, and so on.
Advice: "sendmail" means the generic
/usr/sbin/sendmail tool that all MTAs have, but it also means the original Sendmail MTA (which first introduced the tool)... You will need
sendmail the tool, but do not touch Sendmail the MTA – instead, use OpenSMTPD, Postfix, or Exim4. They're more modern, easier to configure, more secure, and just as powerful.