Postfix is a mail transfer agent (MTA): server software that sends, receives and routes email over SMTP. As an SMTP server, Postfix can also act as a first line of defence against spam bots and malware. It is not a complete mail solution with webmail or calendar, but a building block that is often combined with other software, such as an IMAP server and spam filters. The administrator installs and configures Postfix on servers of their own.
Wietse Venema wrote Postfix in 1997 at the IBM Thomas J. Watson Research Center in New York; the first release followed in December 1998. According to Wikipedia, it is still actively developed by its creator and other contributors. Postfix is open source under the IBM Public License 1.0 and, since version 3.2.5, optionally under the Eclipse Public License 2.0. Postfix is not a hosted service: data stays wherever you run the server, for example in the EU.