Why are some graduate schools' students so much more productive? I'm a math PhD student. I've noticed that graduating students in top 5-10 schools, by the time they apply for postdocs, will regularly have several math research papers and several articles in preparation, usually with senior faculty. In contrast, at my (Research I university) PhD program most students will only graduate with 1 publication - their thesis. I came to graduate school with a solid knowledge of the "standard undergraduate math major curriculum" but no graduate courses, and no real idea of which adviser I wanted or what area of math, and I struggled to get to the current state of knowledge in a specific field. Looking back I don't see how it's possible for me to write several good papers during grad school. I just don't understand the phenomenon that I'm observing. I definitely think that I've worked hard. My guess is that most entering math grad students at top schools will have taken math graduate courses and will have already been reading research papers and know which research projects they want to work on - in other words, they are 2-3 years ahead of the game. 

Question: Is there something fundamentally different about these top programs, independent of the knowledge, work ethic, etc. of the grad students, that makes creating an impressive publication record easier and/or more efficient? Is there some "secret"? What are the underlying mechanisms that allow students at Stanford or MIT to be so much more impressive on average than a student at a less prestigious place?
The "fundamental difference" that you talk about should arise in three things:


The fact that a student made into the top 5-10 schools implies (not perfectly, of course) that the student has acquired a good amount of knowledge in the field and that he or she works very hard. This means the filtering, and thus a difference arises even before the program could start. It's not hard to assume that someone who gets into a top 10 school has worked harder in life to get there (of course, there are always exceptions). Thus, such a student is bound to be more ambitious, and would not settle for that one thesis at the end of their course. 
Even if you're not that ambitious, seeing many peers around you publishing papers may encourage you or add pressure to do exactly the same. In life, we often try to rise up to the standards around us. If you're in a less reputed college with less motivated peers, you might be satisfied with good grades and a thesis. But if you're walking amongst other motivated people, you'd soon feel lesser and try to get on par. 
Good schools attract good faculty. It's much easier to write a research paper and publish it with the guidance of a great professor. 


We can see that the two principal differences arises without any effort on part of the college or university at all and solely because of the peer group. And that's an important factor in academia as much as it is in the real world.