side, room

廂 is composed of 广 (wide, house) and 相 (mutually, each other). 广 is the picture of a house. 相 depicts an eye looking at a tree, meaning comparison. If you want to compare two objects, you need to put two objects side by side, so 相 has the meaning of side. The original meaning of 廂 is side room, now it means side or room.