Is there more to an interface than having the correct methods

So lets say I have this interface:

public interface IBox
{
   public void setSize(int size);
   public int getSize();
   public int getArea();
  //...and so on
}

And I have a class that implements it:

public class Rectangle implements IBox
{
   private int size;
   //Methods here
}

If I wanted to use the interface IBox, i can't actually create an instance of it, in the way:

public static void main(String args[])
{
    Ibox myBox=new Ibox();
}

right? So I'd actually have to do this:

public static void main(String args[])
{
    Rectangle myBox=new Rectangle();
}

If that's true, then the only purpose of interfaces is to make sure that the class which implements an interface has got the correct methods in it as described by an interface? Or is there any other use of interfaces?