What is this type of monitor?
Some services monitor finances, others keep track of passwords and program access... an identity monitoring service looks out for personal information like Social Security number, name, address, birthday and even your past criminal record (or lack thereof). By entering in all of the pertinent information as you begin to use this type of service, you can ensure that it will go through all of it in a timely and consistent manner, looking out for certain instances where it is used; you'll have the results and information that you need in order to take the necessary next steps to stop thieves.
So it just looks through information?
Yes, it looks through all of the information that you give it access to, but while looking through it, it searches for evidence of certain types of activity and sends you prompt alerts when detected. While many of these changes are completely valid and the result of your actions, they may not be and bear investigating if you don't recognize them.
The companies that create services like this make an attempt to understand the needs of their clients by creating programs that will help many people for many years to come. Though they are simplified in the manner that they use to work, there are options so you can choose the level of service that's right for you.