I have written a short description of the observer pattern here: http://www.devcodenote.com/2015/04/design-patterns-observer-pattern.html
A snippet from the post:
Observer Pattern : It essentially establishes a one-to-many relationship between objects and has a loosely coupled design between interdependent objects.
TextBook Definition: The Observer Pattern defines a one-to-many dependency between objects so that when one object changes state, all of its dependents are notified and updated automatically.
Consider a feed notification service for example. Subscription models are the best to understand the observer pattern.