A royalty is formerly known as a monarchy, which is ruled by a king and a queen. Some people still believe in a monarchial government because back in the day they were an easy way for a civilization to rule themselves.
Royalty is a quaint construct of religiopolitical feudalism where a certain blood line was deemed to have exclusive divine right to rule. By extension via favor of royalty, so do lower levels of nobility, and their penchant for marrying only within "blueblood" circles has also resulted in genetic diseases enjoyed only by royalty and nobles. It's a position one is born to, not aspired to.
In Britain, it still exists only because royalty has undue and overwhelming influence over lawmaking in the form of the House of Lords in addition to royal decree.
Most people who are ruled by royalty believe in their royals because they are a quaint vestige of antiquity and are great for the tourist trade.
I'm not so sure that we don't still have that today. Some folks in Washington act as if they are still the King and Queen. It only exists because people wish to tolerate it. It is easier for some to be serfs than to think and provide for themselves.