There are any number of ways to configure a large, free-standing icemaker -- all you need is a refrigeration system, a water supply and some way of collecting the ice that forms.
One of the simplest professional systems uses a large metal ice-cube tray, positioned vertically. You can see how this system works in the diagram below.
In this system, the metal ice tray is connected to a set of coiled heat-exchanging pipes like the ones on the back of your refrigerator. If you've read How Refrigerators Work, then you know how these pipes work. A compressor drives a stream of refrigerant fluid in a continuous cycle of condensation and expansion. Basically, the compressor forces refrigerant through a narrow tube (called the condenser) to condense it, and then releases it into a wider tube (called the evaporator), where it can expand.
Compressing the refrigerant raises its pressure, which increases its temperature. As the refrigerant passes through the narrow condenser coils, it loses heat to the cooler air outside, and it condenses into a liquid. When the compressed fluid passes through the expansion valve, it evaporates -- it expands to become a gas. This evaporation process draws in heat energy from the metal pipes and the air around the refrigerant. This cools the pipes and the attached metal ice tray.
The icemaker has a water pump, which draws water from a collection sump and pours it over the chilled ice tray. As the water flows over the tray, it gradually freezes, building up ice cubes in the well of the tray. When you freeze water layer by layer this way, it forms clear ice. When you freeze it all at once, as in the home icemaker, you get cloudy ice (see How do you make clear ice cubes? for more information).
After a set amount of time, the icemaker triggers a solenoid valve connected to the heat-exchanging coils. Switching this valve changes the path of the refrigerant. The compressor stops forcing the heated gas from the compressor into the narrow condenser; instead, it forces the gas into a wide bypass tube. The hot gas is cycled back to the evaporator without condensing. When you force this hot gas through the evaporator pipes, the pipes and the ice tray heat up rapidly, which loosens the ice cubes.
Typically, the individual cube cavities are slanted so the loosened ice will slide out on their own, into a collection bin below. Some systems have a cylinder piston that gives the tray a little shove, knocking the cubes loose.
This sort of system is popular in restaurants and hotels because it makes ice cubes with a standard shape and size. Other businesses, such as grocery stores and scientific research firms, need smaller ice flakes for packing perishable items. We'll look at flake icemakers next.