Why must a room air conditioner be placed in a window rather than just set on the floor and plugged in? Why can a refrigerator be set on the floor and plugged in?

Both air conditioner and refrigerator work on the principle of reverse Carnot cycle. Heat from the system is extracted using work done and is transferred into the surroundings.

In case of air conditioner heat from a room is extracted and is released into the surrounding.

In refrigerator the heat from the container or food is extracted and released into the surroundings.

Now air conditioner is used to cool a room. It takes the hot air from the room and releases it outside the room. If it is placed inside the room then the heat extracted from the hot air will be rereleased into the room making the room hotter.

So, they have to be placed somewhere it can release it outside the room, and hence the optimal placement is near a window.

Now the refrigerator is used to cool food which has less heat energy inside them so it is not necessary to keep it in position where heat has to be released outside the room. The heat released is very less and hence will not have considerable effect on the room temperature.