All your provinces on whatever continent you move the capital to (and anything on a different continent but with a land connection) will start generating normal tax and production income, and your old home provinces will now be colonies generating tariffs and have -90% tax income.
Also, importantly, if someone now occupies your original provinces in a war, they won't give you war exhaustion and will be worth hardly any warscore since they're distant overseas. They'll have to come to you in the New World in order to significantly hurt you.
Also you'll lose the Colonialism CB if the continent where you moved was the only place you bordered other countries' colonies; you have to have overseas provinces adjacent to their overseas provinces to get it.