A relatively small number of people became infected with HIV – 51 of the 8,197 people given the vaccine, and 74 of the 8,198 who received dummy shots – but the difference was statistically significant, which means scientists believe it could not have happened by chance. It worked out at a 31% lower risk of infection for the vaccine group.The only quibble I have with the above is with the "could not have happened by chance" statement; it would be more accurate to say "is very unlikely to have happened by chance." The alpha value is chosen somewhat arbitrarily. In educational research, it's most often 5%, meaning that (on average) one in twenty times you say "the results are unlikely to be due to random chance," you're wrong and the results are due to random chance. Medical research typically sets the bar higher, with an alpha value of 0.5% or even 0.05%, meaning that your likelihood of identifying random results as meaningful is only 1 in 200, or 1 in 2000, respectively.
Still, the article above stands out as one of the nicest bits of science/health reporting I've seen in a while, in terms of allowing the interested reader to see the structure and meaning of the research.