An extension method in C# allows developers to add new functionality to an existing type without modifying the original types source code, creating a new derived type, or recompiling the original type. It is a special kind of static method defined in a static class, where the first parameter of the method should be the type being extended, prefixed with the "this" keyword. This special keyword tells the C# compiler that this is an extension method.

Extension methods are called as if they were instance methods on the extended type, even though they are static methods. For example, if you have an extension method with the same signature as an instance method, the compiler will always bind to the instance method. When the compiler encounters a method invocation, it first looks for a match in the types instance methods. If no match is found, it will search for any extension methods that are defined for the type, and bind to the first extension method that it finds.

To create an extension method, you need to define a static method inside a static class. The extension method can be added to your own custom class, .NET framework classes, or third-party classes or interfaces. Extension methods cannot access private members of the extended type, and they do not participate in inheritance or polymorphism.

In summary, an extension method in C# is a way to add new functionality to an existing type without modifying the original types source code, creating a new derived type, or recompiling the original type. It is a special kind of static method defined in a static class, where the first parameter of the method should be the type being extended, prefixed with the "this" keyword. Extension methods are called as if they were instance methods on the extended type, even though they are static methods.