In a statically cooled cabinet, the evaporator is a cold plate, wall or set of tubes with no fan. Air touching it cools, becomes denser and sinks; warmer air rises to take its place. This slow natural circulation cools the cabinet gently. Most chest freezers work this way, with refrigerant tubing wrapped around the inner liner.
Static cooling is quiet, simple and dries food less, because air moves slowly over it. That suits unwrapped cakes, some display cases and long-term frozen storage in chest freezers. With no fan there is also less to fail and less energy used by the cabinet itself.
The drawbacks are slower pull-down, slower recovery after door openings and more temperature variation from top to bottom, especially in tall upright cabinets. Static evaporators also collect frost that must be removed by manual defrost from time to time. For a busy kitchen reach-in opened dozens of times an hour, fan-forced cooling is usually the better choice.