REEFER is a contraction of "Refrigerated Container" and will keep the contents at a pre-configured temperature, often -18 degrees C for "deep frozen" items like meats. Items like fruits need to be chilled to perhaps +4 degrees C, and not frozen.
The bodywork is lined with extra insulation, and there may be humidity control systems to protect the contents. A nominal "20 foot container" or TEU will have slightly less internal capacity when it is refrigerated compared to a normal sized container due to insulation and motor. The motor is outside the storage space, its in a separate protected area at one end of the container.
Here are some stacked reefers, mixed in with regular shipping containers (also known as "sea cans")
The white ones have a motor pack visible on the end, which are connected to an all-weather power socket. This is charged as an additional cost when booking space on a vessel. Trucks also have power ports to run the motor.
The motor runs a compressor which is connected to an evaporator and condenser. There are often fans to increase airflow over both.
In the context of this story, a reefer is an ice-box or ice-coffin for preserving a living person for a long voyage. The Reefer is probably a "plug and play" unit with a lot of self-contained systems, requiring only power to function. It may have an internal power source as backup for some amount of time, or it might be independent of ship's power.