Exim is a mail transport agent (MTA). With Exim, you can:
get a message from some programs (cron, for example) via e-mail. This is especially useful if you are root, because you can see such a message (usually an important error message) even if you are not logged in to your machine when the error happens.
send an e-mail to a user on your machine without an internet service provider (ISP).
use fetchmail, which fetches mails from a POP (Post Office Protocol) server.
use procmail, a tool for distributing e-mails you received to right folders (directories) automatically before you read them.