In a clinical trial, there is always a possibility that the effect seen may have occurred by chance. Confidence intervals are a useful approach to assessing the role of chance.
Consider the following scenario. A trial is being carried out to investigate the effectiveness of drug A in preventing heart attacks. 10 patients receive drug A, and 2 of these patients have a heart attack within the next 12 months. 10 patients receive placebo and 3 of these patients have a heart attack within the next 12 months.
Drug A has reduced the risk of a heart attack by one third, in other words, a relative risk reduction of 33%.