SMTP

Simple Mail Transfer Protocol. This is the protocol that you exchange mail with between two mail hosts. Program that accepts mail with this protocol is called a MTA (Mail Transfer Agent). The SMTP uses TCP usually on port 25.

You don't collect mail from your home computer through this scenario, although you can if you really wish. In place of SMTP you would retrieve your mail with POP3 or IMAP.

SMTP works in conjunction with DNS and has its own resource record for the delivery of mail. The SMTP resource record is called MX for "mail exchange" and it can be given a priority for mail delivery.

Accepting mail at home with SMTP
Pretend you have a static IP and wish to receive mail at home with SMTP instead of POP3, you can set it up that another computer receives your mail while you're offline and delivers it whenever your computer comes back.

Given a set of priorities for example your computer has priority 1 while the other has priority 2, every mail agent will attempt to deliver to the highest priority then the next highest until it can deliver mail or it queues it. The next highest knows that it should not attempt to deliver the mail and instead wait for the highest priority to come back online, then it will deliver the mail.