Why do we need interfaces in Java?

I would say the main use is polymorphism, or the ability to perform the same operation on a number of different objects. If different objects all implement the same interface and have the same method, you can store all of those objects in a Vector, for example, and iterate through the Vector calling that method on each one.

I was also thinking about how interfaces are used. I hope this will help others:

An interface is a contract (or a protocol, or a common understanding) of what the classes can do. When a class implements a certain interface, it promises to provide implementation to all the abstract methods declared in the interface. Interface defines a set of common behaviors. The classes implement the interface agree to these behaviors and provide their own implementation to the behaviors. This allows you to program at the interface, instead of the actual implementation. One of the main usage of interface is provide a communication contract between two objects. If you know a class implements an interface, then you know that class contains concrete implementations of the methods declared in that interface, and you are guaranteed to be able to invoke these methods safely. In other words, two objects can communicate based on the contract defined in the interface, instead of their specific implementation.

Secondly, Java does not support multiple inheritance (whereas C++ does). Multiple inheritance permits you to derive a subclass from more than one direct superclass. This poses a problem if two direct superclasses have conflicting implementations. (Which one to follow in the subclass?). However, multiple inheritance does have its place. Java does this by permitting you to "implements" more than one interfaces (but you can only "extends" from a single superclass). Since interfaces contain only abstract methods without actual implementation, no conflict can arise among the multiple interfaces. (Interface can hold constants but is not recommended. If a subclass implements two interfaces with conflicting constants, the compiler will flag out a compilation error.)

from: http://www.ntu.edu.sg/home/ehchua/programming/java/J3b_OOPInheritancePolymorphism.html#zz-6.6

In addition to these responses I would say the most important use for interfaces is to reduce coupling between components in your software.

An interface allows to represent an agreement between classes on how they will talk to each other without being tied to the actual implementations.

This allows us to replace implementations by others (very useful for testing, or changing use cases) without changing the compiled code.