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.
For Wood Elves, growth is called Kindreds.
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.