The term "pump priming" is derived from the operation of older pumps; a suction valve had to be primed with water so that the pump would function properly.
Note: According to Investopedia, the phrase "pump priming" was originally used during the Herbert Hoover presidency:
The phrase originated with President Hoover's creation of the Reconstruction Finance Corporation (RFC) in 1932, which was designed to make loans to banks and industry. This was taken one step further by 1933, when President Roosevelt felt that pump-priming would be the only way for the economy to recover from the Great Depression. Through the RFC and other public works organizations, billions of dollars were spent "priming the pump" to encourage economic growth.
The theory of it being necessary to stimulate aggregate demand in an economy has been shown faulty by Austrian school economists. SEE: The Failure of the New Economics by Henry Hazlitt,