@mosaic - It all depends on how you configure the monitor. The most basic option is a simple ping request (similar to running ping -c 5 yourdomain.ext from the CLI). If the service (i.e. UptimeRobot or NewRelic) receives a valid response (i.e. one that doesn't signal a timeout), the service is deemed to be responsive and another check will be performed in X minutes (5 minutes for UptimeRobot, as an example).

You can, however, also configure the request to scan a page for certain text. Ideally and preferably, this would be text that does not change. An example would be text within your HTML footer (such as Copyright 2014-2015 YourDomain/YourCompany - All Rights Reserved). If this text is not found when the check is performed, the monitor will often run another check to validate the first response before sending an alert. If multiple checks fail, then the alert will be sent to via the method of your choice (i.e. e-mail, SMS, etc).

UptimeRobot allows for a decent amount of customization in terms of how the checks are performed. More advanced configurations can be achieved by simply setting up more monitors (since they allow you to create up to 50 for free). You could use one to check Port 80 (the default HTTP port), one to scan the homepage, one to scan another page etc.