What do programmers mean when they say, “Code against an interface, not an object.”?

Consider:

class MyClass
{
    //Implementation
    public void Foo() {}
}

class SomethingYouWantToTest
{
    public bool MyMethod(MyClass c)
    {
        //Code you want to test
        c.Foo();
    }
}

Because MyMethod accepts only a MyClass, if you want to replace MyClass with a mock object in order to unit test, you can’t. Better is to use an interface:

interface IMyClass
{
    void Foo();
}

class MyClass : IMyClass
{
    //Implementation
    public void Foo() {}
}

class SomethingYouWantToTest
{
    public bool MyMethod(IMyClass c)
    {
        //Code you want to test
        c.Foo();
    }
}

Now you can test MyMethod, because it uses only an interface, not a particular concrete implementation. Then you can implement that interface to create any kind of mock or fake that you want for test purposes. There are even libraries like Rhino Mocks’ Rhino.Mocks.MockRepository.StrictMock<T>(), which take any interface and build you a mock object on the fly.