A number of skeptics argue that one reason for some charters' success is that they skim some of the best students from traditional public schools. Matthew Yglesias fundamentally misunderstands this argument (as, I suspect, do many others) in this post on recent research on KIPP when he writes that the authors are "able to look in a rigorous way at whether the high performance of KIPP students relative to demographically similar non-KIPP students is merely the result of some kind of selection effect".
While it's true that some charter schools do attract students who score higher, on average, than their peers, no serious education wonk is arguing that this alone is why the KIPPs of the world have higher test scores (which is not to say that nobody is making this argument). Indeed, if we look at research on these high-flying charters -- note, I said research and not the popular press -- the statistics cited aren't usually snapshots of how many kids passed a certain test but, rather, longitudinal examinations of the growth of kids' test scores over time. In this sense, simply having higher achieving kids from the start wouldn't help much -- and could conceivably hurt a school.
So what is meant by "selection effects" then? Well, when skeptics argue that charters often skim off the best students, they mean best students in a more holistic sense. If you ask a teacher to identify their best students, they wouldn't just point you to the kids with the highest test scores -- they'd point you to the kids who worked hard, cooperated, asked questions, turned in assignments on time, showed up every day, and generally did what was asked of them. And having a school full of students in this mold would make teaching easier, hallways quieter, and a school's climate more positive -- all of which would aid student growth.
As far as I know, there hasn't been much research on whether charters do, in fact, recruit and retain kids who are "better students" in this sense (please note that I'm not saying there hasn't been any, only that I'm unaware of it -- and, actually, if you know of some I'd appreciate it if you sent it my way). But there's plenty of reason to suspect that at least some charters' student bodies might skew in this direction. Probably the most cited reason is that it takes extra effort for a parent to enroll their kid in a charter school -- making it quite logical to assume that more motivated parents are more likely to fill out the application (of course, maybe the parents' motivation is driven by hatred or their current school or something rather than desire for their kid to excel). Secondly, there are various indicators that some charters are more likely to give kids the boot, or at least threaten to do so, than are traditional public schools. For example, I watched one video in which a KIPP principal walks in the first day of school and tells a kid who's not cooperating that if this school isn't for him that he can leave -- that's not something that traditional public schools can really do.
Anyway, the point is this: when people talk about charters benefiting from "selection effects" they're talking about schools enrolling "better students" in the sense that they're more motivated and more cooperative, not that they simply enroll higher-scoring students. I don't know whether or not charters actually have better students, but it's easy to imagine that a more enthusiastic, better behaved student body would make a school far more productive.