A daemon is a program that runs in the background, rather than under the direct control of a user. If you are more familiar with DOS or early Windows, this kind of program would be known to you as a TSR (Terminate and Stay Resident) program. In NT systems, you would refer to these as services.
Loosely speaking, a daemon is any process that runs in the background (instead of interactively). If an interactive process such as a shell is used to start the daemon, the daemon continues to run after the interactive process is closed. In FreeBSD, daemons are ordinarily started by init at bootup, and stopped by init at shutdown.
Unix users might use the name daemon and service with rough equivalence, especially when speaking to a general audience. A "unix service" is never a daemon (it usually means that access to a unix system is provided), whereas a "Windows service" always means a daemon-like process.