There are many situations where the water demand on a well water system exceeds the production capacity of the well. For instance, 10 gpm is typically considered the minimum flow rate needed to adequately supply a single family residence. But what if the well only produces three gallons per minute? That three gpm totals quite a lot of water over a 24 hour period (4,320 gallons, were the pump to run continuously) and a non-pressurized storage tank can make that well quite capable of satisfying the water needs of that residence.
Another example would be a property that has a well with enough capacity to supply the normal needs of the residence, but local fire codes require that the homeowner have a water connection that will provide 60 minutes of water at 50 gpm and 45 psi. In this case, it makes sense to install a well pump that is sized to the performance of the well, pump into a large non-pressurized storage tank, and use a booster system to provide the needs of the residence and fire department.