A “cocktail hour” is an “hour” when “cocktails” are served, but many other things besides cocktails can be served (soft drinks and hors d’oeuvres, for example) and the time can be longer than one hour (5-7 p.m., for example). A cocktail hour is often a socializing time set after work and before a dinner.
 
“Cocktail hour” is cited in print from at least 1895 and the tradition appears to have started in New York City, especially in fashionable clubs and restaurants. For many New Yorkers, the cocktail hour was the time just after work when the nearest bar was visited before returning home. The “cocktail hour” tradition was threatened in 1919 during the start of Prohibition, but the tradition formally returned in the 1930s when Prohibition ended.
     
 
wiseGEEK
What is Cocktail Hour?
Hosts of informal dinner parties or receptions may want to schedule a time of pre-dinner socializing know as a cocktail hour. Guests who arrive during the cocktail hour are often treated to hors d’oeuvres or light snacks, along with an assortment of mixed alcoholic drinks, wines and beers. A professional mixologist may be hired to prepare the drinks during more elaborate events, but quite often the host will play the role of bartender during the cocktail hour or the guests may serve themselves.
 
If the cocktail hour is intended to be an occasion in itself without a dinner to follow, the guests may be served what is best described as “heavy hors d’oeuvres.” Heavy hors d’oeuvres often include substantial foods as sandwiches, meat dishes and pastries. If a dinner is planned, guests may enjoy lighter fare such as chips and dip or vegetable platters. The cocktail hour may also be limited to a specific type of drink, such as Bloody Marys or Margaritas.
 
The purpose of a cocktail hour is to provide invitees with an atmosphere conducive to informal socializing and mingling, not to create a roomful of intoxicated guests. Hosts should provide music suitable for the occasion, along with plenty of opportunities for comfortable seating and casual eating. A good cocktail hour should put all the guests in a receptive mood for the dinner event itself. An extended cocktail hour also allows early birds and the fashionably late to both be satisfied.
 
(Oxford English Dictionary)
cocktail hour n.
1927 E. HEMINGWAY Men without Women (1928) 68 Sometimes, after the *cocktail hour.
1930 A. BENNETT Imperial Palace xiii. 78 ‘Not quite the cocktail hour here, is it?’ said Sir Henry.
1966 Observer 13 Nov. (Colour Suppl.) 40/2 The Cocktail Hour, commonly known as drinks time, is a mysterious 6-8 p.m., limbo.
 
5 July 1895, Omaha (NE) World Herald, pg. 3:
TEA VS. COCKTAILS.
(Harper’s Weekly.)
(...)
The way to get a cup of afternoon tea in New York is to call at some house where it is habitually given. but sometimes the thirst for the tea and the desire to make a call are not contemporaneous. To buy a cup of tea is inconvenient. It can be done at a club. It is down (done?—ed.) in the clubs occasionally and it is not an absolute novelty to see a man who thinks his reputation can stand it pouring himself a cup of tea from a specially ordered pot as he sits among his alcoholic fellows at the cocktail hour.
 
Chronicling America
3 January 1903, Paducah (KY) Sun, pg. 4, col. 3:
As Davies says, “It was cocktail hour and all was still.”
(From the New York Sun. Also in the Perry, Iowa Daily Chief, October 9, 1902, pg. 2, col. 4—ed.)
   
27 May 1904, Fort Worth (TX) Star-Telegram, pg. 4:
AMERICAN POSSIBILITIES IN PARIS.
New York Press
It begins to look as if the boulevards of Paris and the litlte tables set before the cafes on the sidewalks, surrounded by groups sipping their coffee, would remind Americans newly arrived in the French capital of Fifth avenue or Sherry’s and Delmonico’s at what New Yorkers sometimes call the “cocktail hour.”
 
4 December 1904, New York (NY) Times, “The Man in the Street,” part 4, pg. 5, col. 1:
IT was in what has been called the power house of the Stock Exchange, in a basement on New Street, at the crowded cocktail hour just preceding the exodus homeward from the financial district, the other afternoon, that Jacob Field met a gentleman who had borrowed a hundred dollars from him many months before and had since broken many promises to pay.
     
Google Books
To-morrow in the East
By Douglas Story
London: Chapman & Hall, Ltd.
1907
Pg. 58:
In the club at the cocktail hour — from noon till one o’clock — all the men of English-speaking Shanghai, the brokers and the bankers, the piece-goods merchants and the shipping agents, crowd about the bar and barter the news of the day.
 
Google Books 
The Novels, Stories and Sketches of F. Hopkinson Smith
New York, NY: Charles Scribner’s Sons
1908
Pg. 115:
The cocktail hour had now arrived — one hour before dinner, an hour which was fixed by that distinguished compounder of herbs and spirits, Mr. Biffton—and the room began filling up.
 
28 November 1908, Waterloo (Iowa) Daily Courier, “The Tangled Web” by Ethel Watts-Mumford Grant, pg. 10, col. 7:
Alice banged the door. “You make me tired, Kate. Don’t you recall that rhyme of Tennyson’s or somebody’s—
 
“‘Between the dark and the daylight—
When the night is beginning to lower,
Comes a pause in the day’s occupation
That is known as the cocktail hour.’”
(The original poem is “The Children’s Hour,” published in 1860 by Henry Wadsworth Longfellow—ed.)
   
Google Books
Knocking the Neighbors
By George Ade
Garden City, NY: Doubleday, Page & Company
1913 (Copyright 1911, 1912)
Pg. 144:
Along about the Cocktail Hour he would find himself sitting first in one Chair and then in another, but he Cashed big every Morning when he awoke and found that Henry Katzenjammer was not sitting on the Foot-Board making Faces at him.
 
11 May 1919 Idaho Statesman (Boise, ID), pg. 9:
“COCKTAIL HOUR”
UNRECOGNIZED BY
NEW GENERATION
New York Institution Becomes
Only Tradition to Younger
Business Set; Takes Too
Much Time and Money Now.
By HERBERT COREY.
NEW YORK—Last time Harry Leon Wilson was in town he went out on a seeing-New York trip. He always does when he comes to New York. It is a rite. he walks from his hotel to the next hotel and sees what he sees and then goes back to his hotel and tells his wife about it and they begin to telephone the information desk about trains out of town. Unless detained by business he can see all of New York that he wants to se in half an hour.
 
“Just the same that it used to be,” he told his wife. “Not torn up quite so much, perhaps, and the women are using a different colored powder—sort of yellow.”
 
Old Cocktail Hour Gone.
There are differences, though. Three years ago a bartending friend of mine on Thirty-fourth street used to go to the hot room after his work ended each day and have his arm scientifically rubbed by a masseur. The miscles were kinking. Then he had a list of 40 cocktails and was too busy to talk. Customers fought their way to the bar and got their’s as a favor and fell back to make room for others. Now he leans over the same bar in an agreeably discursive mood most of his watch on. he says the old cocktail hour has become a tradition. The rising generation does not drink as the fallen one did.
 
“It takes too much money,” says he. “Whisky at 35 cents a ashot means that a fairly healthy man invests a lot of money in a real jag. Anyhow, the kids don’t drink as their daddies did.”
 
Google News Archive
16 May 1919, Pittsburgh (PA) Gazette Times, pg. 16, col. 3 ad:
Will the cocktail hour survive the cocktail?
Will men continue to gather about the small round table when tea and the nut sundae replace the highball and the Bronx?
(E. M. Statler, a chain hotelkeeper, in the June American Magazine—ed.)
 
14 April 1962, Dallas (TX) Morning News, “The Cocktail Hour: A Blessing or a Bane”” by Helen Bullock, section 1, pg. 10:
Where thousands of New Yorkers make it a part of their daily routine to have a few drinks in a bar after work, the average social drinker in Dallas celebrates the cocktail hour in his own home.
 
Thus he gets his driving done before he begins his drinking.
 
In Dallas the cocktail hour is also observed at hotel or home parties, and in many private clubs.
(...)
Some wags in Washington refer to such cocktail-hour conversations as capital punishment.