It seems to be a widely accepted fact among demographers--professionals and amateurs alike (and of amateurs taking an interest in demography, too)--that, assuming net migration of zero, a TFR of 2.1 is the threshold a society must reach if it is to maintain its current population size going into the future. A TFR lower than that portends a numerically attenuated future; a TFR higher than that a correspondingly accentuated posterity. Since first seriously thinking about differential fertility rates after reading Pat Buchanan's Death of the West as undergraduate, I've lazily accepted the 2.1 figure without making an effort to grasp why it is such instead of being the putatively far more easily comprehensible 2.0. People much smarter than myself took no issue with the figure, so why should I?
Resolved to have at least three kids so that I can go to the grave knowing that while my side has lost the war of the womb (yeah, I'm engaging in some oh-so audacious augury, I know) at least I'll know that on my little square of turf I advanced the cause, fait accompli be damned. Still, natal thoughts prodded me to finally want to understand why having two apparently wouldn't even qualify as fighting the forces of desolation to a draw.
Well, for fans of industrialized, developed, first-world East Asian- and European-descended modern market-oriented countries, the news, at least with regards to the figure required for replacement (actually realizing said slightly reduced figure is another story entirely) is good. Our replacement figures actually fall in between 2.0 and 2.1, and are, sans immigration, moving closer to the former and away from the latter with each passing day, thanks in large part to steadily increasing life expectancies and declining infant mortality rates. On the other hand, in more vibrant parts of the world, 2.1 doesn't cut it. In sub-Saharan Africa, in fact, it doesn't come close.
The lower maintenance mark for Icy places relative to Sunny spots results because TFR is a synthetic figure (meaning it is a statistical artifice rather than a measure of any specific population segment at any given time) defined succinctly by Wikipedia as "a measure of the fertility of an imaginary woman who passes through her reproductive life subject to all the age-specific fertility rates for ages 15–49 that were recorded for a given population in a given year". In other words, women who live to at least their fiftieth birthdays not only have to pull their own weight but also have to pick up the slack of those who bite the dust before hitting the half-century mark; more slack for the unfortunate ones who die in infancy and in prepubescence, but also some slack accounted for by those, in decreasing order, who die in their teens, twenties, thirties, and forties.
In the US, more than 95% of women who were born fifty years ago are still alive today (so those of you Xers and millennials who spend an inordinate amount of time speculating on eschatological matters--you know who you are!--stop it, there'll be plenty of time for that later, for now, worry about breeding). A societal collapse notwithstanding, the percentage of those born today who will reach the big 5-0 will be even higher than that. And while 19 in 20 American women born fifty years ago are still around today, nearly 199 in 200 babies born in the US today will make it through infancy.
Sex-selective abortions are another factor pushing the TFR replacement threshold up in other places relative to where it rests in the West, a non-negligible factor in the world's two most populous countries, China and India, nations where the total population sex ratio is more skewed in favor of men over women than nearly any other country on earth, the few exceptions being mostly small islands with large laboring populations like Bahrain (and the norm being a total sex ratio favoring women over men). Oversimplifying, if your tribe has 60 men and 40 women, if each woman has two kids during her lifetime, when the next generation turns over, your population will have declined from 100 people to 80. Conversely, if your tribe has 40 men and 60 women, and each woman has two kids, your tribe will have grown from 100 to 120. The female sex is the limiting factor when it comes to reproduction, after all.