Aquifers are measured by three criteria: capacity, permeability, and porosity. The first is a measurement of an aquifer's total capacity to hold water. The second is how easily water flows through the aquifer; it's dependent both upon the mineralogy (some rocks hold onto water molecules more strongly than others) and the third criterion: porosity. Porosity is how much space to hold water there is per unit volume of aquifer. Obviously, an aquifer with larger pores (small holes within it in which water can accumulate) will hold more water per unit volume than one with smaller holes; larger pores also often—but not always—mean greater permeability, too. A highly porous stratum can be thought of as being sponge-like in construction, if not actual material. Aquifers are created when a porous stratum of rock or sand becomes overlain with one or more impermeable strata.
Most people who've studied physics know that liquids are nearly incompressible. During the creation of an aquifer stratum, water is trapped in its porous material. When topped by other strata, the hydrostatic pressure of the water trapped in the aquifer can, in part, support the load of overburden. This is especially true for highly porous aquifers.
Regardless of whether an aquifer is recharged (by rainfall or groundwater through a region where a portion of the aquifer is exposed to surface water; what hydrologists call a zone of recharge), pumping too much water from an aquifer (e.g., faster than it can be recharged) will significantly reduce the hydrostatic pressure within the aquifer. For a highly porous, spongy aquifer, this loss of structural support within the aquifer stratum coupled with the weight of the overburden can cause the pores to collapse into themselves. On the surface this is experienced as subsidence.
Okay, thanks for the science lesson, Brian. What's the point?
When an aquifer collapses, it permanently loses capacity. No amount of water flowing into the aquifer—if any—is going to be able to generate sufficient pressure to lift the overburden and restore the porosity of the aquifer. In other words, once collapsed, then permanently collapsed; those farmers who are pumping dry Central Valley aquifers—many of which do recharge, albeit slowly—are destroying those aquifers. Even if the rains come, those former aquifers will never again be available in times of future drought.