The interface ensures that you at least get the methods you are expecting; being aware of the definition of the interface ie. all abstract methods that are there to be implemented by any class inheriting the interface. so if some one makes a huge class of his own with several methods besides the ones he inherited from the interface for some addition functionality, and those are of no use to you, its better to use a reference to a subclass (in this case the interface) and assign the concrete class object to it.
additional advantage is that your code is safe from any changes to concrete class as you are subscribing to only few of the methods of concrete class and those are the ones that are going to be there as long as the concrete class inherits from the interface you are using. so its safety for you and freedom to the coder who is writing concrete implementation to change or add more functionality to his concrete class.