I haven't had time to read the published papers, but I imagine the participants were randomised into two equal groups (of many thousands), one of which was given the vaccine and the other a dummy injection (placebo). They will then have been followed to see how many in each group contracted covid-19. A result of say 95% protection would then mean that the number of subjects who contracted covid-19 in the vaccine group was only 5% of the number that contracted disease in the placebo group. So in a trial involving tens of thousands, the numbers might be large enough for a high degree of statistical significance.