Importance of keeping the electricity network frequency stable
The electricity network has several generators (e.g. power stations, or perhaps a solar panel on your roof)

If all these feed into the same network, they must be in phase or instead of providing power they would be taking it.

Lets freeze the AC used in the network in time and make a small DC model: 

Imagine two AA batteries of the same voltage in parallel, + to + and - to -, no problem there.

Now make them 180 degrees out of phase by connecting them + to -, you will have a small explosion.

The +/-0.5 degree limit is how much the network can stand being out of phase due to the resistance and inductance of the connecting cables limiting the power being reflected back by an out of phase node.