Alert messages are report that are sent as the content of your alert notification.
So when an alert is triggered, the report is run and the text that it produces sent in your email or SMS notifications.
Not only does this let you create a completely custom notification format, but it also allows you to send current information - such as temperatures, tank levels etc - in the body of your notification message.
To create a alert message, you'll need to first create a report.
It is very important to keep the report small if you plan on transmitting it via SMS. As large SMS messages must be sent as a sequence of messages, sending large notifications this way can become very expensive.