The higher amount of growth in the province, the faster it receives a population surplus. There’s also the amount of growth a province has per turn. It should say ‘administration’ where it displays the province’s growth and current population surplus points. You can see this information when clicking on a province you own and looking over the detailed pop-up on your UI to the lower-left portion of your screen.
A province has a population surplus after a certain amount of growth throughout several turns.