Imagine you have a lamp in your room that is plugged into the wall with a cord. The electricity from the cord makes the lamp turn on and give you light so you can see in the dark. This electricity doesn't always come in smoothly like a river flowing, sometimes it comes in little jumpy waves like a bumpy road.
Sometimes, when your lamp is on and this jumpy electricity comes in, it can make the light in your room seem to flicker or go up and down really quickly like a heartbeat. This flickering can be annoying, and if it happens too much, it can even make you feel sick or dizzy.
This flickering can happen in bigger buildings too, like offices or stores, where there are a lot of lights plugged into the wall. It can also happen to bigger machines that need electricity to work, like factories or hospitals.
Power-line flicker is just a fancy way of saying that there are jumpy waves in the electricity that make the lights, machines, or other things plugged into the wall flicker. People who work with electricity try to make it come in smoothly, like a river, so that things don't flicker and everyone can see and work properly.