“Emoluments” is just an elegant word for corruption, at least in our Constitution. The framers were particularly worried about foreign powers bribing or trying to influence the infant republic. Their solution was to allow gifts, money and the like to be accepted by members of the executive branch only if Congress approved. Put differently, one of the constitutional duties elected lawmakers take on is the responsibility to prevent the corruption, or appearance of corruption, by foreign powers of the executive branch.
Every president until this one has voluntarily complied, jettisoning foreign businesses and assets and/or asking permission to receive foreign gifts.