A “mover and shaker” is someone with power and influence in a particular field. Arthur O’Shaughnessy’s “Ode” (1873) contains the line, “Yet we are the movers and shakers/ Of the world for ever, it seems.” Mabel Dodge Luhan’s book Movers and Shakers (1936) further popularized the term, but widespread usage appeared in the 1950s.
 
A “mover and shaker” has also been called “Very Important Person” (VIP) in the United States since at least the 1940s.
 
   
Wiktionary: mover and shaker
Noun
mover and shaker (plural movers and shakers)
1.(idiomatic) someone who has power and influence in some field or activity.
2.(idiomatic) The people in an organization who are most responsible for getting things done
 
Merriam-Webster Dictionary
mover and shaker noun
plural movers and shakers
Definition of MOVER AND SHAKER
: a person who is active or influential in some field of endeavor
First Known Use of MOVER AND SHAKER
1951
 
(Oxford English Dictionary)
mover, n.
colloq. (orig. U.S.). A person who initiates events and influences people; a dynamic and influential person. Chiefly in mover and shaker (after quot. 1873).
1873 A. O’Shaughnessy in Appletons’ Jrnl. 4 Oct. 440/3   Yet we are the movers and shakers Of the world for ever, it seems.
1892 Harper’s Mag. Feb. 431/2,  I know that Chicagoans boast that theirs is the most mixed population in the country, but the makers and movers of Chicago are Americans.
 
shaker, n.
One who or something which shakes (in the transitive senses of the verb). Also in phr. mover and shaker, shaker and mover (U.S.), a person who influences events, a person who gets things done.
1874 A. O’Shaughnessy Music & Moonlight 1   Yet we are the movers and shakers Of the world for ever, it seems.
1972 F. Knebel Dark Horse (1973) ix. 124   The rich movers and shakers‥always manage to manipulate the Congress for their own benefit and screw the rest of us.
 
Google Books
4 October 1873, Appletons’ Journal, pg. 440, col. 3:
AN ODE.
(ARTHUR O’SHAUGHNESSY.)
We are the music makers,
And we are the dreamers of dreams;
Wandering by lone sea-breakers,
And sitting by desolate streams;
World-losers and world-forsakers,
On whom the pale moon gleams;
Yet we are the movers and shakers
Of the world for ever, it seems.
 
Google Books
Music and Moonlight: poems and songs
By Arthur O’Shaughnessy
London: Chatto and Windus, Publishers
1874
Pg. 1:
ODE.
WE are the music makers,
And we are the dreamers of dreams,
Wandering by lone sea-breakers,
And sitting by desolate streams;—
World-losers and world-forsakers,
On whom the pale moon gleams;
Yet we are the movers and shakers
Of the world for ever, it seems.
 
OCLC WorldCat record
Movers and shakers
Author: Mabel Dodge Luhan
Publisher: New York : Harcourt, Brace, 1936.
Series: Intimate memories / Mabel Dodge Luhan, Vol. 3. 
Edition/Format:  Book : English : 2nd printing
 
9 December 1951, New York (NY) Times, “Science; Literature”:
These are just three of the many movers and shakers of our time who have never been rewarded, in spite of all the astoundingly elaborate system of ... 
 
Google News Archive
29 November 1952, St. Petersburg (FL) Times, “Truman’s Farewell Address” by Stewart Alsop, pg. 8, col. 5:
WASHINGTON—Washington is a city peopled by ghosts. The new great—the men who will soon wield immense power in this capital of the free world—are almost all elsewhere. The former great, the movers and shakers of only a few weeks ago, now seem actually to have shrunk in physical size, and even to have become faintly transparent, so that one looks nervously at a Cabinet officer, to make certain that the furniture behind him does not show through.
 
Google News Archive
2 February 1953, St. Petersburg (FL) Times, “Why Democrats Are Reviving” by Joseph and Stewart Alsop, pg. 6, col. 3:
For the first time in 20 years the bountiful southward flow of White House patronage has been cut off. What is more, the great movers and shakers of the recent past, the chairman of powerful committees—Southerners almost to a man—are movers and shakers no longer.
 
Google News Archive
15 August 1956, Milwaukee (WI) Journal, “‘Hostess With Mostest’ Wines, Dines VIP’s,” pg. 3, col. 6:
The Democratic movers and shakers filed up marble stairs of the Blackstone hotel through a police cordon and an orchid trimmed velvet rope, which were little help against a mob of watchers jamming the lobby and sidewalk.