echo $MAIL is linux executable script that shows weather you have an new mail or not. When you type #echo $MAIL on the prompt, it will print the location if you have a mail.
For example, I have a cron job that will remind a user on Step 24th at 12PM to "Do not forget to pay your taxes" This will be emailed to users mailbox at 12PM on Step 24th. But what if the user is not logged in? Then user will not know if he has a message in his mailbox. So when he types echo $MAIL on the prompt, he will know that he has a massage in the mailbox.
So if I have a cron job or a script that runs on every time user logs in, the user will know that he has a mail in the mailbox.