I have been reading the Gang Of Four, in order to solve some of my problems and came across the Mediator pattern.
I had earlier use
In the original book that coined the terms Observer and Mediator, Design Patterns, Elements of Reusable Object-Oriented Software, it says that the Mediator pattern can be implemented by using the observer pattern. However it can also be implemented by having Colleagues (which are roughly equivalent to the Subjects of the Observer pattern) have a reference to either a Mediator class or a Mediator interface.
There are many cases when you would want to use the observer pattern, they key is that an object should not know what other objects are observing it's state.
Mediator is a little more specific, it avoids having classes communicate directly but instead through a mediator. This helps the Single Responsibility principle by allowing communication to be offloaded to a class that just handles communication.
A classic Mediator example is in a GUI, where the naive approach might lead to code on a button click event saying "if the Foo panel is disabled and Bar panel has a label saying "Please enter date" then don't call the server, otherwise go ahead", where with the Mediator pattern it could say "I'm just a button and have no earthly business knowing about the Foo panel and the label on the Bar panel, so I'll just ask my mediator if calling the server is O.K. right now."
Or, if Mediator is implemented using the Observer pattern the button would say "Hey, observers (which would include the mediator), my state changed (someone clicked me). Do something about it if you care". In my example that probably makes less sense then directly referencing the mediator, but in many cases using the Observer pattern to implement Mediator would make sense, and the difference between Observer and Mediator would be more one of intent than a difference in the code itself.