A Crêpe Suzette is a crêpe (thin pancake) served warm folded in half or four with a warm orange sauce on it.
Generally, the sauce is made of carmelized sugar, orange zest, orange juice, and an orange-flavoured liqueur such as Grand Marnier, and brandy. The slight bitterness of the orange zest counteracts the sweetness. The brandy is lit to burn off some of the alcohol and to meld the flavours in the sauce.
In restaurants, Crêpes Suzette are usually finished at the table in a chafing dish  so diners can see the spectacle of the flambéing of the sauce. (The actual crêpes are prepared in advance in the kitchen.)
There is, though, another method to prepare them, as defined by Escoffier in his 1903 Guide Culinaire. The crêpe batter is flavoured with curaçao and mandarin orange juice. A compound butter (beurre suzette) is made of creamed butter, sugar, mandarin orange juice, mandarin zest, and curaçao (the curaçao used is the clear, obviously — not the blue.) The crêpes are cooked, then while still hot spread with the butter, folded into four, and then served hot. There is no sauce, apart from the melting butter, and no flambée that happens.
 More usually now, a shallower dish called a “Crêpe Suzette” dish.
Some people say that Crêpes Suzette were invented by Escoffier. Others say they were named after French actress Suzanne Reichenberg (1853-1924) at the Marivaux restaurant in Paris in 1897, by Joseph, the proprietor. Still others say that they were named after the Princess de Carignan by chef Jean Redoux.
That aside, the French chef, Henri Charpentier (1880 – 1961) repeatedly laid claim his entire life to being the inventor of Crêpes Suzette, even providing the occasion and time of their creation. He repeated the story in such detail and so often that to look for another origin one must call him an outright liar.
It was 65 years ago, but Henri Charpentier, one of the last of the great chefs, remembers that breakfast on the terrace of the Cafe de Paris in Monte Carlo as if it were this morning. That’s the day he created Crêpes Suzette. Charpentier is 81, and now it takes four years to get a reservation at his tiny restaurant. But let him tell the story of that breakfast, and where it led:
“I was only 16 and serving the Prince of Wales, son of Queen Victoria, later King Edward VII of England. Among the diners at the Prince’s table was a beautiful French girl named Suzette. I cannot recall her last name. It does not matter. His highness ordered crêpes — the French pancakes. I mixed the sauce, and added a brandy blend of my own. As I did, the heat of the chafing dish accidentally set the simmering cordials afire.
“I was embarrassed but I did not show it. I poured the fiery sauce of the crêpes, as if the flames were set on purpose. The prince tasted. Then he smiled and said: ‘Henri, what have you done with these crepes? They are superb.”
“I was thrilled and offered to name them in his honor. But he declined. ‘Henri,’ he said, ‘we must always remember that the ladies come first. We will call this glorious thing crêpes Suzette.’
“That was the day, monsieur. People had been eating pancakes from the days of Napoleon — even the Romans, but never before that, day crêpes Suzette.”
For the record, Charpentier used the sauce method, as opposed to the beurre suzzette method. 
Plural: Crêpes Suzette (s after Crêpe), not Crêpe Suzettes.
 Bacon, James. Kitchen Still First Love of Veteran French Chef. Petersburg, Virginia: The Progress Index. 5 April 1961. Page 21.
 “THE FINE NONCHALANCE of Henri Charpentier, the courtly, white-mustached originator of crepe suzettes, in his excellent new restaurant (tucked away in the Park Dearborn) as he pours Cointreau and brandy directly from the bottles without measuring it but with a great flourish, into the pan for the sauce . . the lusciousness of the sauce AND the crepes.” — Cass, Betty. Day by Day: Impressions of Chicago. Madison, Wisconsin: Wisconsin State Journal. 5 May 1942. Page 13.
Clay, Xanthe. With a flame in your art. London: Daily Telegraph. 17 February 2007.