China's decision to (further) relax its infamous one-child policy is, as much as anything, an economic decision.
China put the one-child policy in place decades ago, when the country feared a destabilizing population boom. It benefited in the short run — the country slowed its population growth and got a boost to growth since it didn't have as many children to support. Today, China faces a different problem: a precipitous decline in the ratio of working-age people to total population.
This is bad news for the economy as a whole — working-age people are the engine of any economy — and it's especially worrisome for a generation of elderly who don't have big families to support them.
As the graph shows, this phenomenon is familiar in much of the developed world. But it's especially problematic for China because, despite all the hubbub about economic growth, China is still a poor country, and it can't afford the kind of social safety net that's common in the developed world.