A nation's population expands every day regardless of other statistical factors or decisions made by the government. For the first five days of gameplay, a nation's population will jump by 1-2 million per day, and by as little as 4 million or as much as 8 million per day after that. It takes roughly six months of consistent activity for a nation to reach 1 billion persons. Population increases are random, and are neither slowed down nor accelerated by the effects of daily issues or WA resolutions. The only thing that can stop population growth is ceasing to exist. Once a nation is resurrected, population growth will resume from the point it left off at when it died.
Reaching certain levels of population unlocks new opportunities for nations, including what sorts of issues the nations can receive, and the ability to further customize national settings. For example, reaching 500 million enables nations to submit issues and customize their pretitle. Reaching 250 billion, 750 billion or 1 billion allows nations to receive new issues to name the leader, capital or state religion. Having 500 million also assures your nation's name will be retired and unable to be reused if the nation ceases.
Since population increases are a bit rapid and/or dramatic to have any realistic basis in roleplay, RPers typically set their national populations at a more modest number and ignore the gameside increases. Increasing your population unrealistically, or to give your nation certain advantages over others, is considered a form of wank.
A region's "population" can be either the total number of nations in a region, or the combined total of those nations' populations. If each nation in a region of five has 200 million, then that region's combined population is 1 billion. These numbers are unofficial and are calculated by offsite calculators and NSwiki.