Selection has favoured, over the past four billion years or so, organisms that reproduce themselves. This has resulted in the evolution of behaviours that tend to lead to reproduction.
Peez
Sure, that's a given, but doesn't answer the question. The question is
which specific qualities evolved in us that cause the behavior?
I'm not sure exactly the sort of answers you are looking for. But at least for some people, it manifests as a deep desire to have children. Have you heard the term "baby crazy" before? While it's mostly a bit of a joke - a woman hits 30 then all of the sudden they cannot stop talking about having kids, or wanting to stop and hold every baby they see. But it is quite common for young couples to marry in their late mid 20s with solid plans about how and when they are going to start a family, but then a couple of years into the marriage, the woman will abandon those plans and want to "wing it." At more extreme examples, you have straight up baby kidnapping, and even more pathological,
fetal kidnapping.
My own sister never had kids, she's much older than me, in her early 40s. But definitely, when she turned 30, she was pretty nuts about kids. It was actually quite sad, because she really really desired the whole traditional marriage with kids sort of deal, but she ended up dating one asshole who just wasted her time. I guess to be fair to him, he was apparently always clear about not wanting kids. I think she just held out hope that eventually he would. There were at least a couple of guys she could have married in her mid-to-late 20s. At that point, though, I don't think the urgency of her biological clock had caught up to her. That changed around her late 20s and early 30s, when she became pretty damn obsessed.
I just turned 29 (and I'm a male). For the last year or so, I've noticed that seeing babies makes me a lot happier that it ever did. Before, it was more-or-less a mundane thing, but now, I want to hold them and find myself smiling uncontrollably when I make eye-contact with one.