The Growth of a province, horde army or Black Ark is a measure of the expansion of its population. Growth leads to the accumulation of Population Surplus, which is required when upgrading a settlement or horde army.
For hordes, growth is called Horde Growth, and population surplus is required for most buildings, not just upgrading the horde/settlement. For Black Arks, growth is called Black Ark growth.
Growth and population surplus can be seen on the Province Info panel, or the Building panel if playing a horde faction. Growth in a horde or province can be stimulated by certain buildings and commandments, and can be hindered by enemy raiding, corruption and heroes.
The population surplus costs for upgrading a settlement are shown on the settlement building rollout on the province Overview panel. More building slots become available when a settlement is upgraded.