Demographic momentum. This came up a bunch of times in the China Population post on IO9, and explaining it got too long for a comment. Also, it's a hell of a pet peeve of mine, because it's really an incredibly basic concept.
If you have a country where everyone has six children for a while, and then they start having one child, the population of that country should shrink, right? Yes, eventually. A pretty long eventually, actually. The population of China, for example, is still about twenty years away from reaching it's peak, much less shrinking, and they've had sub-replacement (less than ~2.1 children per woman) birth rates for decades already.
That is, the population of China has continued growing since they introduced the one child rule 40 years ago, and it will continue to grow for 20 more. Despite the fact they have really not been having very many children.
This is because of "demographic momentum," and it is kind of a bitch. What happened (and in enough places is still happening) in the last half century or so is the demographic transition: populations grew very quickly because of much lower child mortality, before society caught up and started having fewer children. So most of the developing world has found itself with a lot of children and young people.
These young people, now that they're adults, are not having a lot of kids. They don't want them and they're not having them - but there are a lot of these young people. If woman only has 1.7 or so children, that's still a lot of children - who's parents are alive, and who's grandparents are also mostly alive. This next generation, the 1.7 per-couple, is still much, much larger than it's grandparent or great-grandparent population.
(The age pyramid has gone from being pyramid shaped in 1970 to Christmas tree shaped in 2010. The young women of 1970 had fewer children than the young women of 1960, so the bottom rungs of the pyramid shrink. But there are more 1970-women than 1960-women, so when the babies of 1970 start having their own children, in the 1990s, the pyramid flares out again.)
Compare China to Eastern Europe. Eastern European birthrates crashed down to sub-replacement in just 1990, but Eastern European countries are already showing actual shrinkage. This is because even before 1990, birthrates were low. They didn't go from 6 to 1, they went from 2 to 1. The age pyramid was already an age column - the new, small generation is smaller than the grandparent generation it's replacing, because those grandparents didn't bother to have many children that would have gone on to create their replacements.
Remember - that's who new babies are replacing in the population count - their elderly grand, and great-grandparents, not their 20-45 year old parents, who are alive and well. It's only when those cohorts - the parents - start dying that it will change. The generations that were born during the demographic transition, the generations that got big before they started producing the generations that got small. Then total populations will actually start shrinking. And we're a while away from that.
FYI, globally, we're not going to start shrinking until about 2050, and that's with very optimistic assumptions about further drops in birthrate (the global average is already only 2.4.) More likely we'll keep growing (slowly) at least until 2100, reaching a population of close to 10 billion. Barring some completely science fictional technological/social developments, this is going to happen. No amount of harping about birth rates in third world country or tsk tsking about dwindling resources is going to change it. These people will be here - their parents have already been born.
I recommend the UN 2012 Revision on Population Prospects (Sorry, PDF. It's the UN, what can you do?) for a pretty fun read. Well, I think it's a fun read.
Also, this site for checking out age distribution and country-level growth prospects.