The mains frequency is literally how fast the generators in power plants are turning. If the load on the grid increases, those generators slow down slightly and more natural gas/coal/heat needs to be added to increase the frequency again. This whole process is quite complicated as not every plant can react in the same time. Some plants are always at 100% capacity, while others are dedicated to governing the frequency.

So there are small fluctuations, often between 0.2 Hz around the base frequency, but the average is very close to the theoretical 50/60 Hz. And for an alarm clock that is good enough.