It's as Doug summarizes above. If you don't have any guarantee your children will survive to adulthood, if you don't have a guaranteed pension, if you live in a situation (usually rural) where children contribute economically, then you are compelled or induced to have a large family for survival reasons. Betsy Hartmann's _Reproductive Rights and Wrongs_ is a good source on this.
With the outlawing of child labor and the rise of compulsory education--as happened, for example, in the U.S.--children are no longer contributing economically, they become an individual cost. (Of course, in a waged situation, children are no longer undercutting the wages of their parents, which is a plus.)
With a drop in infant and child mortality, and some other way to secure your old age than the support of your children, family size tends to drop independent of access to more advanced forms of birth control. This is where the population controllers got it all wrong, based on a disrespect for the capacity of the poor to analyze their own situation. It isn't just disrespect, though, it's also (what we hope is a justified) fear of growing numbers of peasants and workers who want to overthrow same population controllers and their rich sponsors.
Jenny Brown