Hazard ratios are basically numbers that tell you what the risk of getting a disease are in two separate experimental groups. If I have a control group that doesn't eat chocolate and an experimental group that eats one bar of chocolate per week, and the chocolate eaters get heart disease 0.9 times as often as the non-chocolate eaters, my hazard ratio is 0.9. If there's no difference between how often each group gets heart disease, the hazard ratio is 1. And to go along with my hazard ratio, I provide something called a 95 percent confidence interval, which is the possible error in calculating the hazard ratio. The confidence interval gives you the range of numbers that you can be confident the hazard ratio falls within. So if I have a hazard ratio of 0.9 with a 95 percent confidence interval of 0.85-0.95, that means there's a 95 percent chance that the actual hazard ratio is between 0.85 and 0.95.