The term doggy bag denotes a bag, provided on request by the management of a restaurant, in which a diner may take home any leftovers.

These leftovers were originally intended for the diner’s pet dog, according, for example, to the following by Otto R. Kyle in his column By the Way, published in the Decatur Daily Review (Decatur, Illinois) of Wednesday 10^th June 1953:

Guy Lombardo* who is kept busy filling orchestra engagements when not doing a long stand at the Roosevelt Grill in New York City, opened a restaurant in Freeport, Long Island, a few years ago and has a “Doggie Paks” special for diners who want to take left-overs home to their dog.

(* Gaetano Alberto ‘Guy’ Lombardo (1902-77), Canadian-American bandleader and violinist of Italian descent)

An inhabitant of Dayton gave the same explanation in a letter published in the Journal Herald (Dayton, Ohio) of Thursday 24^th May 1956:

“Have you ever eaten a delicious dinner and had to leave a nice steak bone, or some chicken, when you have a little dog or cat, waiting for a snack at home? Well, my only trouble is—I don’t leave it. I take it home. Sometimes boldly, sometimes not so bold . . . but there are times that I feel so criminal, just as if I were snitching some of the silver!
“I visited in a city in Indiana, lo and behold when we finished dinner, our host asked for a doggie-bag and the waitress not only brought a large waxed paper bag but gathered all our steak bones together for his pet.
“Our hostess set the bag on the floor beside her and I almost cooed with delight. They didn’t have to sneak around a bit. Can you go to bat for this for us here?”

The earliest occurrence of doggie pack that I have found is from the column The Lyons Den, by Leonard Lyons, published in The Montgomery Advertiser (Montgomery, Alabama) of Monday 7^th April 1952; Lyons mentioned the term without giving any explanation:

Larue’s customers now may take their unfinished meat courses with them, wrapped in a fancy package tagged “Doggie Pack.”

The earliest instance of doggy bag that I have found is from the review of the White House, a restaurant in Golden Valley, a suburb of Minneapolis, by Will Jones in his column After Last Night, published in the Minneapolis Sunday Tribune (Minneapolis, Minnesota) of 19^th December 1954:

The president’s cut is two inches thick and fills a platter. They brag it’s the biggest cut of prime ribs served anywhere in these parts, and I believe them. Our whole family could have made a meal of it.
They cut seven servings from a 23-pound rib roast. Before roasting, they trim some of the extra fat from the meat, and then wrap it around the roast to supply juice to the less fatty parts.
The meat was a uniform pink from edge to edge. Succulent as it was, I had to leave almost half of it.
Well, not really leave it. I asked for a paper doggy bag and took it home. It made swell sandwiches the next day. All the dog got was bare bones.