Corned beef is beef that is first pickled in brine and then cooked by boiling. Usually, cuts of meat are used that feature long muscle grain, such as the brisket.
The name corned beef is due to a coarse salt being used in the pickling. Corn originally meant grain, as in a small particle of something, and referred to the corns of salt. A similar, but more highly-spiced meat, is pastrami.
Corned beef is often regarded as a "deli" meat; that is, often purchased at delicatessens. A special sandwich type that is still fairly popular is the Reuben, made with corned beef, cheese, sauerkraut, and thousand-island dressing.
(Note that the Reuben entry calls for Russian Dressing, however both are delicious.)
Fifty pounds of beef, three pounds of coarse salt, one ounce of saltpetre, three-quarters of a pound of sugar, two gallons of water. Mix the above ingredients together and pour over the meat. Cover the tub closely.
(from The Household Cyclopedia 188819th Century corned beef recipe
