Alerts let you configure some pre-defined actions that will generate an email to you alerting to you of what is going on. One example is a reminder when the server isn't up to date for a new release of CrushFTP. Or a notice when a drive is getting low on disk space, or anytime a user changes their password or gets low on quota space...you want to know.
Alerts are global, where the user events are specific to a particular user and event type.
One useful alert item is the catch invalid email attempts. This is useful if you send out automated emails based on user input for example on an upload. If they type the email wrong, no one would know the email was never delivered. You can do an email like this in the event to handle this (the variables will be filled in with the emails contents):
From:%from% To:%to% CC:%cc% BCC:%bcc% Subject:%subject% Error%result% %body%