Observer is a pattern where an object called the subject maintains a list of dependents (observers) and notifies them of any state changes. I implemented this recently to log changes to an Account object, and to notify the account holder if their account had expire - here's the basics of the code, hopefully it'll help someone else figure out how the pattern works
The basis of the Observer pattern is that you attach these "observer" objects to a main object. These watch the object and see if something changes (like a property value) and react accordingly. For their example, they create a setup that extends the main Observer class to have some or the detection functionality built-in.