As far as I know, secondary fluid usually will be used whenever the pipeline is long enough. Use of of direct vapor compression for these applications would cost a lot due to the price of refrigerant, environmental issue in case of leakage, and price of electricity for running compressor(s).
I suggest to read about ice rink as an applied example of using second medium in industry.
In addition to the previous answer. The use of chilled water in air conditioning is essential when the not all the rooms and areas are required to be air conditioned in the same time, for example in hotels and hospitals.
DX cooling systems is small units when compared to chilled water cooling systems, and that is because the former units (DX systems) will needs higher amounts of refrigerants charges when it is bigger in size leading to higher cost systems and an increase in maintenance of leakage problems. Therefore, DX systems are preferred in small or moderate size applications like restaurants and small halls. Chilled water system is commonly used in big size application like hotels and hospitals and so on.
I agree with the other answers that water is used as a secondary cooling medium when the system is bigger. But in my opinion that is not the whole answer, because there are the so called VRF systems (variable refrigerant flow) for buildings with many rooms. These systems work with very small refrigerant content. The main disadvantage of these systems is that it is very difficult to create a comfortable indoor climate because of the (very) low evaporation temperature of these systems. Temperature of the supply air can go down to 6°C or lower. There is no diffuser that is capable of mixing this cold air without extreme draught.
Therefore buildings that are to be designed for a high level of occupant expectation and/or high energy efficiency will be equipped with a secondary cooling based on water.
In addition to the previous answers.The Direct Expansion (DX) and Chilled Water central air conditioning plants are both used at different places depending on the applications and size of the place to be air conditioned. Let us see the comparison of DX and chilled water central air conditioning plant. Normally chilled water system has been preferred where the height is too much or building needs multi-functional options as well as long life system. DX are normally used in small commercial buildings with tenants or small residential units. If the demand load is very huge for example1000s of tonnage then chilled water is used. Direct-expansion (DX) equipment uses refrigerant as the liquid medium. Regardless of the liquid medium used, the liquid is delivered to the cooling coil at a cold temperature. In the case of direct expansion equipment, the air passing over the indoor cooling coil heats the cold liquid refrigerant. Since the more the demand, the more is the requirement of compressor of VCR system which in turn requires more demand for Electricity. (Compressors consume a high rate of power for running). However, the capital costs of both types of systems become comparative after about a cooling load of about1000kW. (This figure varies greatly depending on the site layout.). There are no pressure loss problems in the chilled water system. In this system chilled water is pumped by the pump at very high pressure, which is good enough to carry it to various floors of the multi storey buildings.
In addition to the previous answers, notice that chilled water systems allow to avoid vapour condansation in room air by controlling water temperature above dew-point.
Moreover, water systems allow to use components from different manufacturers, while direct expansion systems require a combined control of compressor unit and expansion valves that usually imply the adoption of components from a unique manufacturer with problems in maintance if the specific components are not available anymore