Factory method is a GoF design pattern which is widely used. The official definition says
The Factory Method Pattern defines an interface for creating an object, but lets the subclasses decide which class to instantiate and Factory Method lets a class defer instantiation to subclasses.
Basically Factory method pattern provides the solution for what the Simple Factory couldn't achieve as I mentioned in the previous post, ie. fulfilling the Open-Close Principle. This is achieved by providing an interface with a method for creating objects between Client and Concrete Creator classes. This particular method is known as the "factory method". (Here the interface I'm referring to is from a design view point, technically it can be a class or an interface in java)