A major power, also known as a great power or world power was a nation which was powerful enough to exert influence on a global or a galactic scale.
In 1968, in response to a nuclear warhead being placed in sub-orbit by another major power, the United States launched a suborbital platform with multi-warhead capacity for the purpose of maintaining the balance of power. After the launch of the rocket, Gary Seven had deviated its flight path and armed the warhead. Lieutenant Nyota Uhura detected military alerts from the major powers on Earth who were beginning to worry. As the rocket drew closer to impacting in Eurasia, Chief Engineer Montgomery Scott reported that all major powers were on full missile alert, and that a retaliatory strike was ordered on warhead impact. (TOS: "Assignment: Earth")
World War II ended with the United States taking its place as a dominant world power and cultural influence in the second half of the 20th century. (TNG: "Manhunt")
In the 2360s and 2370s, the great powers of the Alpha Quadrant included the Cardassian Union, the United Federation of Planets, and the Romulan Star Empire. (DS9: "The Circle", "The Search, Part II", "Inquisition")
In 2370, Minister Jaro Essa likened the Bajoran people to doormats; they had been stepped on by any great power that happened by, such as the Cardassians and the Federation. (DS9: "The Circle")
In 2375, Ru'afo noted that in the past twenty-four months, the Federation had been challenged by every major power in the quadrant, which included the Borg, the Cardassians, and the Dominion. (Star Trek: Insurrection)