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Interfaces were also a central part of COM, which was a very successful technology for separating interfaces from implementation.
In C++ you could have an abstract class with no implementation, and you could inherit multiple classes. Java and C# got rid of multiple inheritance, so in order to have the ability to inherit multiple contracts (not behaviors), they created interfaces. You can only inherit one class in C#, but you can inherit as many interfaces as you want.
An interface is jst a contract. It says which members that an instance must implement. It does this, however, without implementing any default behaviors.
It's just another layer of abstraction. Not really sure where it came from.. I still often hear them called contracts rather than interfaces.