If you add load to a generator, it increases the amount of force needed to turn it. (There's a nice experiment with a hand crank generator that has a switched load - it's very noticeable, and logical - the electrical power you use needs to come from somewhere).

If the amount of force that's available doesn't increase, the generator slows down. The generators are synchronized to the grid. Of course, as the frequency drops, power plants regulate by applying more force to the generators (e.g. increasing the amount of gas or water fed to a turbine).