Can someone explain the population of Humans in SC?

I doubt that the Terran population is still rapidly increasing. Keep in mind that almost all Dominion Terrans at least( we don't know about the Umoja or Kel-Morian worlds) are retreating to the Core worlds, if not being butchered by the zerg. Fertility rate is likely to go way down given the sudden increase in population density and relative decrease in resources per capita.
Assuming total abandonment of the fringe worlds and total stability of the core worlds, and that the core worlds are roughly the same size and living conditions as earth, we should be sitting pretty at roughly 60 billion people (Earth is projected to have 10 billion people in a couple of decades, but this is definitely not sustainable. Maybe the Terrans have access to better pollution reduction?). I'd add maybe another couple of billion refugees from the fringe worlds (accepting more than that would be like the United States today suddenly accepting another 385 million people across their borders, which is ridiculous).

Regarding how population could have grown so quickly from 32,000 to however many billion in such a short time: Humans have exponentially grown from the industrial age to the present day, and that was with many hurdles and obstacles in the way. It's likely that the terrans having a) modern medicine b) near unlimited resources given the unrealistically large number of habitable planets around Tarsonis, Moria, and Umoja, would have growth much, much faster than what we experienced in the 1800's. It's also possible that since the Terran governments of the Confederacy, the Dominion, and the Kel-Morian Combine aren't exactly governments that respect human rights, forced fertilization (or, at least heavily encouraged) of the female population to raise more children for the workforce and army are possible. Nazi Germany actively encouraged women to have as many kids as possible, and even today countries like Italy and Norway are subsidizing public education, healthcare, and the practice of maternity leave in an effort to increase their dwindling populations, so it's not impossible to speculate that the Terrans might have done something similar.

 

Only modern terrans have that kind of tech, not the originals.