Especially used of a new product or idea, the phrase under wraps means known to only a few people, secret.

This phrase originated in horse racing: under wraps is used of a horse that the rider is holding back and intentionally keeping from running at top speed; G. Clark Cummings explained the origin of this horse-racing term in Under Wraps (American Speech – December 1956):

The Blood-Horse (a weekly magazine devoted to the turf) in its issue of March 12, 1955, stated that the term under wraps was generally used ‘in a literal sense to indicate that the rider had wrapped the reins around his hands in order to obtain sufficient purchase on the leather to restrain the horse from full speed.’

The earliest instance of the horse-racing term under wraps that I have found is from The Chicago Daily Tribune (Chicago, Illinois) of Sunday 28^th May 1893; the previous day, a brown colt named Domino, owned by James R. Keene, had won the great American Stakes:

It had been expected that Domino would go out at once and spread-eagle the field, and when it was seen that Dobbins was by his side, two lengths back of Despot, passing the old club house those who played the brown colt on Keene’s own statement of “Billy” Lakeland, that he was the fastest and quickest to move he had ever trained, got nervous. But they had no reason to fear. Taral had the colt under wraps, and as the horses swung into the stretch with Despot in front he cut loose. At the same moment Lambley made his move with Dobbins. Garrison was working his passage through the ruck with Joe Ripley. The others were not in it. Just as soon as they got straightened out Domino began to draw away from his field and the farther they went the greater his lead became. Taral could have pulled him to a walk and won, but he took no chances, keeping the brown brother to Correction going until the wire was reached.

The phrase under wraps came to be used in other sports; for example, the following is the beginning of Dixie II Will Try to Break Motor Boat Record To-day, published in The Brooklyn Daily Eagle (Brooklyn, New York) of Tuesday 4^th August 1908:

Motor boat enthusiasts will have an opportunity of finding out this afternoon the correct speed of Dixie II. The craft was fast enough to successfully defend the Harmsworth Trophy yesterday at Huntington Harbor. She went 30 nautical miles at the rate of 32 statute miles an hour, but according to the people on the inside, Dixie was kept “under wraps” during the entire race.

The phrase came to be also used in boxing, as in The Montgomery Times (Montgomery, Alabama) of Friday 12^th August 1910:

The next heavy-weight champion of the world will be a man born and raised in Montgomery, Ala. Dr. F. Caffey, (colored) medical expert for Jack Johnson in his preparation for the big fight, has a young giant, 6 feet, 4 inches high, weighing now 208 pounds, age, 19 years. He has been coached for the past two years by Caffey and has defeated every good man in this section. He has been kept under wraps and has been coached carefully and in two years can defeat any heavy-weight in America, so Caffey says. He will be handled with care and in two years you’ll see a new champion in this young Montgomerian.

The phrase also entered football’s vocabulary; the following is from the San Francisco Chronicle (San Francisco, California) of Wednesday 2^nd November 1910:

Tomorrow will see the first of the final three football games that are to be played on the Berkeley campus during the preliminary season, when the California second varsity meets the team of the University of Southern California Law School. […]
The first California team is being kept under wraps in preparation for the game with the University of Nevada on Saturday.

The phrase came to be also used in baseball, as in the Arkansas Democrat (Little Rock, Arkansas) of Saturday 15^th April 1911:

Cubville pennant prospects this year may depend upon the service of a kid pitcher, as they did last year, when a recruit from the South Michigan League, King Cole, led the league and held the Bearlets in the lead when the veterans were floundering like bewildered elderly persons in the maze of corner traffic.
Cole is in a hospital temporarily, but another kid, Fred Toney, who has been kept under wraps by Manager Chance, was given a warming up gallop the day the team struck Chicago, and against the fast Notre Dame team showed so much class that he is looked upon as another Cole.

There seems to be an early instance of under wraps used as a generic synonym of the adjective secret in the following from The Los Angeles Times (Los Angeles, California) of Sunday 17^th March 1912; this newspaper had apparently acquired a car used in a ‘good roads campaign’ aimed at the building of an ocean-to-ocean highway:

Ready for a good roads campaign that will extend from Los Angeles to New York The Times car will be used this week to organize divisions in Ontario and Pomona. […]
The Times car is now at Alhambra. The next stop will be at Pomona. This car will not be seen again in Los Angeles until its great mission is performed. The high-powered motor will be kept under wraps. No record run will be made. This journey will occupy months but will be thorough.

The earliest instance of under wraps unambiguously used in the generic sense concealed that I have found is from the Real Estate section of The Pittsburgh Sunday Post (Pittsburgh, Pennsylvania) of 14^th January 1917:

Seldom in the history of the buying movements of Pittsburgh property have negotiations been kept “under wraps” as of late.

FOLK ETYMOLOGY

The phrase under wraps, therefore, does not refer to the wrapping placed over newly developed machines before their official launch.