Bradford's law is a pattern first described by Samuel C. Bradford in 1934 that estimates the exponentially diminishing returns of extending a library search.
Here is how it works. Suppose that a researcher has 5 core scientific journals for their subject. Suppose that in a month there are 12 articles of interest in those journals. Suppose further that in order to find another dozen articles of interest, you have to go to 10 journals. Then that researcher's Bradford multiplier bm is 2 (ie 10/5). For each new dozen articles, that researcher will need to look in bm times as many journals. After looking in 5, 10, 20, 40, ... journals, most researchers quickly realize that there is little point in looking farther.
Different researchers have different numbers of core journals, and different Bradford multipliers. But the pattern holds quite well across many subjects, and may well be a general pattern for human interactions in social systems. Like Zipf's law, to which it is probably related, we do not have a good explanation for why it works. But knowing that it does is very useful for librarians. What it means is that for each specialty it is sufficient to identify the "core publications" for that field and only stock those. Very rarely will researchers need to go outside that set.
However its impact has been far greater than that. Armed with this idea and inspired by Vannevar Bush's famous article As We May Think, Eugene Garfield at the Institute of Scientific Information in the 1960s undertook the development of a comprehensive index of how scientific thinking propagates. The creation of his Science Citation Index had the effect of making it easy to identify exactly which scientists did science that had an impact, and which journals that science appeared in. It also caused the unexpected discovery that a few journals like Nature and Science were core for all of "hard science". The same pattern does not happen with the humanities or the social science - possibly because objective truth is so much harder to establish there.
The result of this is pressure on scientists to publish in the best journals, and pressure on universities to ensure access to that core set of journals. With everyone armed with the same list, the definition of what journals were best became very important. And, of course, publishers had the same list, and therefore knew which journals they could charge more for. Which tightens pressure on universities, because when they have to spend more on the core journals, libraries have less latitude to buy other journals. And if they don't buy them, then papers in them do not get read, and therefore don't get cited, thereby making publication in them worth even less, tightening the spiral.
This price spiral has become known as the Serial Pricing Crisis.
It has been argued that this problem with peer-reviewed paper journals is currently in the process of being replaced by electronic publishing.