Drawing of an artesian well. An artesian aquifer is an underground layer which holds groundwater under pressure. This causes the water level in the well to rise to a point where the pressure is equal to the weight of water putting it under pressure.n aquifer is a geologic layer which can hold water such as sand and gravel, limestone, or sandstone, through which water flows and is stored. An artesian aquifer is trapped between rocks or clay which causes the pressure.