Financially, this means providing for them into their mid-20s, often at least through (and including) college. The costs of everything along the way -- housing, clothing, food, education -- continues to grow and outpace income growth.
The other big resource is time. You're expected now to enroll your children in a variety of activities and shuttle them around, rather than give them unstructured time to roam. Families now are more disconnected from their extended families and their communities, so it's harder to get help here. It's up to the two parents (if they're still together) who only have so much time to give.
Basically, the marginal cost of each kid continues to increase, so people have fewer children.
I think another effect is the extension of many of life's milestones. Establishing a career, getting married, etc continue to fall later and later, leaving people less time to build and raise a family.