Royals are ordinary human being. What sets them apart is basically that their direct ancestors looted, killed and conquered a bit more than yours or mine. And obviously the executions of Mary, Queen of Scots, Charles I, Louis XVI and Marie Antoinette showed their blood is precisely of the same colour as ours.
Tribal leaders, lead warriors, Barons, Lords, Kings and Emperors have all been ordinary people. What set the first ones apart (I mean the founders of dynasties or families) was their courage, leadership abilities or wit; in other words, their people chose someone to represent and/or protect them. Once the selected leader had an heir, the idea was that someone has to do all the ruling/leading, so they might as well go with a known quantity than unknown one.
Leaders of the past tried to give their positions legitimacy by claiming it originated from greater (divine) source. That's the reason so many of rulers of the ancient world, such as Ancient Greece, claimed they had the blood of Gods in their veins; Alexander of Macedonia, for example, was not only presumably descended from 2 of the greatest heroes of the ancient world, Heracles and Hector (and through them - from the Gods, as per legend), but it was also rumoured that Zeus was actually his father as well. European Monarchs continued the trend but with slight modifications; they no longer claimed to be descended from Gods but stated their powers were God given (in other words, they were chosen to Reign by a divine source).
One of the reasons Christianity spread so quickly in Europe and was so readily accepted by local Barons and Kings, was that it suited their agenda perfectly; most of the Christian rules teach respect for authority, knowing 'your place', not asking questions, etc.
As far as the expression "Blue Blood" goes, it originates from the Spanish phrase "Sangre Azul", which was used to describe Spanish Royal Family members in middle ages. The idiom's origin is probably the following; because the Royalty and nobility traditionally had very fair skin (since they didn't have to work outdoors all day), their veins appeared blue through their skin, leading to the belief they had 'blue blood'. Whereas the veins of the working class people were not that prominent, since most of them had very tanned skin (since they did work outdoors all the time to support 'the masters').