They save weight. They don't save a large percentage of the overall weight of the stand, but they make it less top-heavy and therefore more stable when raised high or angled back a long way.
Just to expand on the question of "why not just make it thinner?" - the reason for that is because a thicker sheet with holes will be stiffer than a thinner sheet with no holes with the same amount of metal in. It won't necessarily be stronger in every loading mode - indeed it may be weaker in some - but with a structure like a music stand, wobbliness becomes a problem long before breakage does.