It’s very useful to conceptually understand how Nagios works. The following is a very simplified view on how Nagios works.
Nagios runs on a server, usually as a daemon (or service). Nagios periodically run plugins residing (usually) on the same server, they contact (PING etc.) hosts and servers on your network or on the Internet. You can also have information sent to Nagios. You then view the status information using the web interface. You can also receive email or SMS notifications if something happens. Event Handlers can also be configured to "act" if something happens.