Fertility rate can go down without the number of children being born each year diminishing because of the way it's calculated. There is also the case of fertility lag and several otehr factors to play with it. The net reproduction rate is a more useful tool to see if population reach their replacement treshold, but it's not often used since it takes decades to be calculated. The main cause for lower fertility rate in the industrial world is women getting an education and getting financially established before having children and very low infant mortality. Idealy, you would want, on average, for all women to have two children over the course of their lives to maintain the population stable and avoid problems caused by exponential growth and decline.