from Halo lore:

An arum is a small logic game Sangheili children would play with designed to teach them patience when faced with a difficult problem. It consists of a wooden ball of nested concentric spheres carved from a single piece of wood or other materials. Hidden in its core is a small gem crystal of some kind that could only be shaken free when the player worked out the complex alignment of spheres. To reach the core, each sphere had to be operated in turn to activate the next. No sphere could act without the next one in a hierarchy that was impossible to reorder.

Apart from providing diversion and strengthening character, it was said to represent what made the Sangheili strong: a perfectly-engineered, orderly system that presented a smooth, impenetrable face to the outside world, and each had his appointed place in it.