Welcome to the EMD Forums, nyuszika45!
There are several forums here at EMD, and this thread belongs in the
Fastmail.FM Help and Current Issues forum. Hopefully a forum administrator will move it there.
As Adrian pointed out, IMAP is a protocol used for synchronizing received messages between a server and a local email client on your computer. SMTP is the protocol used to send from your computer through a SMTP server to a destination email server.
Fastmail had a short outage last evening (time at their servers in New York City). I'm sure that is why you had a problem.
Bill