SMTP is the protocol responsible for delivering emails between servers. It is a text-based protocol operating on TCP port 25.
Not all emails need to be delivered between systems. For example, imagine you have a Gmail account. If you compose and send an email to your friend who also has a Gmail account, then SMTP is not necessarily used. In this case, Gmail only needs to copy your email into their inbox (or do equivalent database updates).
On the other hand, consider a case where you send an email to your friend's Yahoo! account. If the email is sent from your Gmail account, then it's clear that the Gmail and Yahoo! servers must communicate. In that case, your email is transmitted from the Gmail server to the Yahoo! server using SMTP.
This connection is illustrated in the following diagram:
Retrieving your email from your mail service provider...
