A Queen and King represents a modern face of her country through the vision that she projects to the world. and when I say 'vision' I do not mean her face, just in in case someone may want to mis-interpret that part of the statement.
Adaptability and modernity are very common terms, just like the terms civility and sophistication. Someone is 'adaptable' if they are able to adjust to their surroundings as necessary. In this case, HM Queen Rania has had to make an adjustment to the World stage and she has had to work with HM King Abdullah in presenting their collective vision of Jordan to the rest of the world.
In my own opinion, someone is considered 'modern' if they exhibit behaviors showing not only adaptability that I have mentioned, but also that they understand that they are not stagnating in a corner (like stagnant water, or unable to move forward); that they are moving in a positive direction in their development -- globally, I believe that both QR and KA have worked very hard to present to the rest of the world that Jordan is a country that seeks development in several areas. As well, they have worked to present and preserve diplomatic interface with western countries. And while there is certainly work to do in many areas (I am sure someone would be more than happy to list all the areas that need improvement), I believe that they have worked very hard to show that their country and their people are an integral part of the world community -- citizens that are deserving of the respect and consideration of other nations. Period.
That is what I mean by adaptable and modern -- some may be very fast to say something like 'those things are redundant!', but ok -- I hope that helps make it clearer.
QR has an integral part in the diplomatic efforts of her country - I will not go into what I mean by the statement that a queen has a diplomatic role for her country, as I believe most may understand that point already.
That is what I mean when I say that QR and of course KA represent their country and adaptable and modern -- or at the minimum, a vision of where they would like to see their country on the world stage.
But again, that is just my opinion