How did world war 2 change the birth rate?

In the USA it increased. In Europe it decreased.

Explanation:

After World War II the birth rate in the United States saw a substantial increase and the generation was born that is known today as the Baby Boomers. Such was the increase in births in the post-war years of economic prosperity that the population pyramid of the United States is visibly larger in the lines marking those years.

In Europe the situation was different. While birth rates had already been decreasing before the onset of WWII, after the war this trend only continued as the continent rebuilt itself after the second of two very deadly conflicts.