What's it measured in?

Quadrillions.

Really we have no idea, billions is probably the most common assumption. It could also be a logarithmic scale (would make the most sense for asteroids), but then we still couldn't tell you how many people are on a given planet.

Without additional lore, we can only speculate. 

Some people, such as me, do not that that "population" is actually a measure of the planet's occupants, but rather a measure of its citizens.  That is to say, population increase represents bringing surface settlements and people under your control.

The biggest problem I have with the literal interpretation of population as a head-count is that this game has a time-scale of, at most, a handful of years.  It's certainly not long enough for multiple generations to pass and therefor the adult population shouldn't actually be increasing much at all.  Even presuming the more ridiculous logarithmic scale, there's no way that the population growth makes any sense in this context.  You can counter with the theory of immigrants, but this raises the very valid question of why people would immigrate into a warzone, or a world enslaved by the Vasari, for that matter.  There are also other valid questions; where does population go when a planet "turns neutral" due to culture?  Who builds and maintains the planetary militia?  Who are the Vasari "enslaving" if the planet was unoccupied before their arrival? 

I feel the most reasonable interpretation of the colonization process is as follows:

All planets are initially occupied by people (most, if not entirely, human in origin) who have small standing militias to protect them.  These people are less technologically sophisticated than the "core worlds" from where the TEC originate, limiting their ability to defend themselves.  When your colony vessel arrives, a small military occupation force is sent to the surface.  This occupation is initially expensive to maintain, but with investment you can build an industrial complex on the surface of the planet.  This would explain underdevelopment tax quite nicely, and the "cities" and "traffic" we see on larger planets would be advanced distribution centers built by the new management.  Orbital bombardment would then not necessarily be indiscriminate killing, but rather a directed assault on the surface-based military installations.  This would also explain militia "bombarding" their own planet; they're attacking enemy invaders who reached the surface. 

What do you mean by an industrial complex?

Infrastructure in a general sense, perhaps? After all, a population won't grow if there isn't the appropriate infrastructure to support that growth (and if it does anyway, it will return back to that maximum by way of unsupported population dying or infrastructure failure).

So Darvin, according to your interpretation, population represents surface settlements that are under your control and the colony ships are actually military transports?

The Sins maunal (as in the PDF file or the hard copy) does say the colony frigates carry colonial adminstrators for the TEC. I believe the Advent have something along the lines of religious figures trained for conversion of the local populace, and I can't remember what the Vasari have. Probably some sort of group trained for overseeing the enslavement of the local population.

Pretty much.

InfiniteVoid, the manuel says "...the Jarun safely ferries civilians critical to the survival of the Vasari species and experienced xeno administrators between the stars."

Darvin, why would the new management build regional distribution centers when they acquired a certain number of settlements?

Relative advantage; you can increase economic productivity by specializing local economies.  The downside is that such specialized economies required highly developed transportation networks to support.  Obviously having a faster, less expensive, and more reliable system is preferable.

Well, what would they be distributing to the natives anyway?

Consumer goods?

The answers to the questions you're asking seem to be fairly obvious/intuitive... I don't see the need to ask them.

Something about taking over planets has always bugged me...

You see, once you've nuked/kinetic-bolted/laser-beamed all ground-based resistance to bits, why doesn't the planet remain a constant drain on your resources? I mean, you've killed a substantial portion of the population, you've taken over their planet, and then you ask them to pay taxes. They're going to fight you, so you'll need to put in a constant stream of cash to make up for all your soldiers and property down there being taken out by rioters, terrorists, protestors, etc.

You get the picture...

It's just that, to me, it only makes sense for the Vasari to bombard from orbit, because they're going to rule through terror anyway, and posibly the Advent, at a stretch, because they could persuade these new people through the Unity that it was all for a good cause.

But the TEC? Unless they're a far more martial force than we've been led to believe, I don't see how they'd keep control of or even benefit from a nuked-out hellhole of a planet.

So Darvin, if the planet elevaters are regional distribution centers,why do asteroid's support only one (and think realistically,please)?

I'd say because the asteroids are supporting a single large center. But again, we really have no idea what population represents, and all that other neat stuff that was discussed in the thread and that I'm too lazy to list here.

 Darvin, if population represents surface settlements that are under your control,how would you explain the Vasari Colony Pods for their Orkulus Starbases?

Those are actually strictly Vasari inhabitants. They are under your taxation policy and add to your credit gain.

I bet they get taxed less than the humans though!