While I am not qualified in this area, the way I understand it is (looking at England here) the queen deals with ceremonies and, as penguin put it, public relations. Also, it probably has something to do with tradition but, I don't know about that for sure. This way the prime minister/parliament have more time to deal with more pressing issues such as making laws and going to war.
I personally believe that this kind of system should be adopted in all areas of the world (especially America). That way Bush can focus more on the war in Iraq and have someone else (like Barbara Streisand or some other ****ty icon like her) greet all of the teachers of the year*.
*My US history teacher won this award and actually said this kind of thing to president Bush while shaking his hand. Also, I would like to point out that this topic is about European leaders so, if you would like to argue about what is best for the US make another topic or something.