Suppose for example you wanted to give the activity a String and have it return a Integer:

public interface MyStringListener{
    public Integer computeSomething(String myString);
}

This can be defined in the fragment or a separate file.

Then you would have your activity implement the interface.

public class MyActivity extends FragmentActivity implements MyStringListener{

  @Override
  public Integer computeSomething(String myString){
   /** Do something with the string and return your Integer instead of 0 **/ 
   return 0;
  }

}

Then in your fragment you would have a MyStringListener variable and you would set the listener in fragment onAttach(Activity activity) method.

public class MyFragment {

        private MyStringListener listener;

        @Override
        public void onAttach(Activity activity) {
            super.onAttach(activity);
            try {
                listener = (MyStringListener) activity;
            } catch (ClassCastException castException) {
                /** The activity does not implement the listener. */
            }
        }

    }