I'm not sure of the name but as I understand it your right, they are large pots that are used as a cistern for storing water. The grass mats keep bugs out and limit air flow that could increase evaporation.

If they are left unglazed and soft fired they are porous and the water weeps out. Keeping the outside damp. In a dry climate having one or more of them on a patio is a primitive form of air conditioning.

Even if glazed and entirely watertight the volume of water also acts as a heat sink, carrying the cool of the night into the day and the heat of the day into what can be a chilly night. The concept works well in high desert environments where the days are hot and the nights quite cold even in summer.