This is actually short for pumped-storage hydroelectricity, which is, undeniably, a bit of a mouthful. Since it is going to become extremely popular, we are told, it seems advisable to have an easier name for it.
The problem for solar and wind energy is that it is in greatest supply in the middle of the day, precisely when people don’t need it as much. So there is a need to store this green energy and make it available at peak periods when people do need it.
The solution is to use the energy to pump water from a low reservoir to a high one. Then you let the water flow back to the lower level through a turbine which releases the energy for use. There is a small loss in the whole operation, obviously, but the loss is not so great, and the gain is highly desirable because the process smooths out the variability in wind and solar energy supply, allowing for the provision of electricity at any time on demand.