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This is part of an assembly (look for ball hinge - ball part) and together it serves as a ball hinge. Originally created to mount small mirrors in an array that can be pointed towards any angle. This assembly also holds it position, so basically it functions like a interior car mirror.
Inside is space for a M4 nut so that this assembly can be mounted on a board. You could als use a screw to fix it on a wall or something. Be aware that the ball part has a tight fit with this one so you need to think of how to assemble these parts.