Gaurav Sood points us to this post, “Why did so many Japanese families avoid having children in 1966?”, by Randy Olson, which includes the excellent graph above and the following explanation:
The Japanese use [an] . . . astrological system . . . based on the Chinese zodiac. Along with assigning an astrological beast based on your birth year, each year also has one of the Five Elements associated with it—all that dramatically affect what your astrological sign entails. . . .
In 1966, however, many Japanese families were still quite superstitious—and . . . 1966 was the year of 丙午 (Hinoe-Uma), or the “Fire Horse.” As one source describes:
Girls born in  became known as ‘Fire Horse Women’ and are reputed to be dangerous, headstrong and generally bad luck for any husband. In 1966, a baby’s sex couldn’t be reliably detected before birth; hence there was a large increase of induced abortions and a sharp decrease in the birth rate in 1966.
Time will tell if superstition will strike again 10 years from now in 2026, the next year of the “Fire Horse” in its 60-year cycle. Given that Japanese is already below the replacement fertility rate (i.e., roughly an average of 2 children per woman), the result could be disastrous.
If you look carefully at the above graph, you’ll see increases during the years before and after 1966. So, while it does seem that the net effect on births is negative, it’s not quite so negative as the spike might make it appear, given that some births that would’ve occurred in 1966 have been displaced to the adjacent years.
Also, I’d like to see the raw data—just total number of births in each year, or I guess even better would be total number of births divided by total number of women aged 15-45 in each country. I’m not saying there’s anything wrong with plotting total fertility rate. It’s just that it’s a derived quantity and it would be helpful to me, in trying to understand it, to see the pattern in the raw data as well.