"Monarch" — What is it?

According to Dictionary.com, a "monarch" is "a sovereign head of state, esp a king, queen, or emperor, who rules usually by hereditary right."  (The citation for this source, as taken from the website, can be found below.)  Well, this certainly answers my question about whether a monarch was solely a king or a queen or any individual and hereditary power... but it still leaves a lot of questions unanswered.  How exactly is a monarchy different from other powers?  When did monarchies come to power, and why are they declining now?  Some countries still have monarchies, but I think they're mostly just for show these days.  Are any countries still under the sole rule of a monarch and his/her family?

England is one of the most commonly known nations that still has a monarch.  Queen Elizabeth II is currently their monarch, but it's also common knowledge that she's mostly just a figurehead — the government system there is headed by a Prime Minister that seems to be much like our President here in the United States.  So why even keep the royal family at all?  Is it a cultural unifier, for diplomacy's sake, or for some other purpose entirely?

I went looking for a list of countries that still have monarchies, and found this list of English monarchs from 1066 to the present.  According to this site, the Norman Conquest brought about the beginning of the English monarchy as we know it, which has been ongoing since that time.  So here are a few more questions: who are some of the most influential and remembered kings/queens of the British Empire?  Why was the Norman Conquest so important?  What was the government in England prior to the Norman Conquest in 1066?  Was there still a king or a queen?

I'm also curious... what's the difference between royals and nobles?  Is there one, or are they just two words that are used for the same purpose?  If they're different, how do they differ, and why?  What is the structure of a monarchy that incorporates a king or queen and then other assorted titled persons?  (I know in the English structure, there are dukes, earls, barons, and so on... how do these figure into the overall structure of government, if at all?)

So I've answered one of my questions, but brought about quite a few more.  Looks like I'll be headed back to research to find as many of these answers as I can.


citations:
"monarch." Collins English Dictionary - Complete & Unabridged 10th Edition. HarperCollins Publishers. 07 Sep. 2010. <Dictionary.com http://dictionary.reference.com/browse/monarch>.