Sendmail is the name of a venerable MTA (or Mail Transfer Agent) still used today on the Internet at large. It is renowned for its arcane configuration files and history of security holes, although modern sendmail has taken great pains to overcome this reputation.
Sendmail understands the SMTP protocol, and others; it does not support reading mail (as a POP3 or IMAP server does). Many enhancements to sendmail exist, for such things as anti-virus scanning in real time, anti-spam blacklist checking, and organization-wide mail routing. Most of these are implemented though the mail filter milter.
All Linux systems typically come with sendmail, or a compatible program, and the major Unix MTAs such as qmail and postfix come with binaries that do "sendmail emulation", allowing them to function as drop-in replacements for sendmail.
If you have trouble because, on bootup, linux hangs for a couple minutes while loading sendmail, see the section on fixing the Sendmail Lock.
The sendmail command
Sendmail is also a command that allows you to send mail from command line, e.g.:
echo "hello world" | sendmail -t email@example.com