In game description:
"This pastry is filled with a sweet bean paste, in 4 flavors combined with a perfect balance. A random jumble of four symbols is imprinted on the top in ancient Growtopian script. Mix this with other Mooncakes in a Laboratory or E-Z Cook Oven to create special Harvest Festival items."
You can get Balance Mooncakes from harvesting trees of any kind but the higher the rarity the higher the chance you can get one. You can also get one (including all the other mooncakes) by purchasing the Harvest Pack that costs 20,000 gems. It is also used to make Songpyeons.