Every developing nation goes through what's called a demographic transition. At the beginning, the standard of living is low and the birth rate is high, but so is the infant mortality rate. As the nation becomes developed, the standard of living becomes higher, leading to improved birth control, healthcare, family planning, people choosing to put having kids on stay for their careers... all these factors lead to a low infant mortality rate and also a lower birth rate due to socioeconomic changes. The transition period in between, where the nation is "developing," is where the population grows the most, caught between high birth rates and lowering infant mortality rates. So when every country's more or less done with this process, the global population stagnates, and the current projection puts that stationary number slightly above 10 billion. More than right now, but not by a lot. The global population won't keep growing the way it is forever, and it's already slowed down by a lot in the last few decades.