need of interface

Lets say I develop a control that among other things supports sorting of class instances. You want to use my control. How am I supposed to know how to sort your particular class when I don't know it even exists?

I could make you inherit from an abstract class of my own - but that makes no sense as it would imply that I am providing a base implementation that you can override if desired. As I have no knowledge of your class there is no real way to provide a base implementation that would be of any use. Also, you would not be able to derive from any other classes (no multiple inheritance in C#).

Alternatively I can provide you with an interface and leave all the implementation up to you. Because I know you will have a Sort method, I can call it from my code without even knowing about your class! All my control needs to do is have a method that takes a parameter of that interface and we all have the result you desire.

An interface is a contract. It tells others that your class supports certain methods - it doesn't say how they are implemented, only that those methods are present. What this means, in practice, is that you can accomplish the same thing in many different ways; absolutely invaluable if you want to use something like Inversion of Control (IoC).

As an example, if you want to use the using pattern in C# then your class must implement IDisposable. Behind the scenes, the compiler translates the using block into the following:

SomeClass someClass = null;
try
{
  someClass = new SomeClass();
}
finally
{
  ((IDisposable)someClass).Dispose();
}

There you see someClass being cast to IDisposable which allows the application to call Dispose.