There is nothing difficult with this word. The original meaning of the word "хозяйство" is household, that is one's house and farm or a plot of land. Hence, "хозяйствовать" means to manage your farm, to keep your house, to run your business. The very word "хозяйство" is derived from the word "хозяин" which means "master", so "хозяйство" also means the property of a master.
Later the use of this word was extended to any enterprise or business, including international economy.