As an example, imagine a frictionless generator with no load, spinning at 60 Hz. The rotating mass of the generator stores kinetic energy, and its windings are ready to convert that to electrical energy. Attaching an electrical load slows the rotation unless something is done to replenish that stored kinetic energy.
On a larger scale, loads are switching on and off all the time. Power plant operators need time to react, because adjusting the throttle isn't instantaneous. A natural gas generator might take seconds to throttle up or down; adjusting a nuclear power plant could take a while. In the meantime, energy is drawn from the buffered kinetic energy of every generator on the grid. They are all rotating in sync because every generator is also a motor.
The frequency of the grid is the signal everyone uses to know whether generation matches consumption, averaged over second or minutes or hours.