The balance of power was when two or more factions or nations were of equal power.
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. Gary Seven noted that this was the same kind of nonsense that almost destroyed the planet Omicron IV. (TOS: "Assignment: Earth")
In 2372, the Kazon-Nistrim stole a transporter module from the starship USS Voyager. Captain Kathryn Janeway claimed the component had the potential to cause vast problems in the Delta Quadrant. Neelix agreed and stated it could alter the balance of power among the Kazon sects who would attempt to get the module and transporter capabilities for themselves. (VOY: "Maneuvers")