A croque-monsieur is a ham and cheesesandwich which is dipped in beaten egg, then pan-fried or grilled (U.S. broiled), and served hot. It originated in France as a fast-food snack served in cafés and bars. More elaborate versions come coated in a Mornay or Béchamel sauce. When topped with a fried egg the dish is known as a croque-madame.
The origin of the name is uncertain but the first part almost certainly derives from the verb croquer (to crunch, or to munch). Its first recorded appearance on a Parisian café menu was in 1910.
According to About.com the word croque comes from the verb croquer or "to crunch".
I make croquesmonsieur (the plural is definitely croquesmonsieur, not messieurs..) often for my dear husband, but since I live in England, I make an English variant of it, with mature (or even extra mature) cheddar, and instead of the bechamel, I just put crème fraîche under the ham on both slices of bread.
I worked out for an hour earlier in the day to prepare for eating my croquemonsieur in the evening, but it was worth it.