Why do we use Interface?
Is it only for Standardization?
Analogy 1: Much like the US space shuttle, Russian Soyuz spacecraft and Chinese Shenzhou 5 can all dock to the International Space Station, because they implement the same docking interface. (This is just an example - I don't know if it's true in real life however let's suspend our disbelief for the sake of an example)
Analogy 2: Like you can plug various computer monitors into your home computer. You can plug a wall-size TV into it, an old CRT (the thick kind), a 20" flat screen, or a braille machine for the blind to "see" by touch. There's compatibility among these various/different devices and your computer because they all agree on interface standards.
Details of C# interfaces -- With C#/OOP interfaces you're doing the same kind of thing but in the unseen/virtual world.
You're correct about standardization, but also flexibility, scalability, extensibility, maintainability, reusability, testability and power.
(The more you use software interfaces the more these "buzz words" will be understood. And always consider interfaces in the real world because they have done us equally well.)