In more detail
Odds are the chance of an outcome divided by the chance of no outcome: a probability of 0.8 is odds of 4 to 1. From a 2 × 2 table with cells a, b, c, d, the odds ratio is (a / b) / (c / d), which equals ad / bc. Values above 1 mean the outcome is more likely in the first group, values below 1 less likely. A confidence interval that includes 1 means the difference could be chance.
Why it matters
Odds ratios are the standard measure for case-control studies and the output of logistic regression. They are easy to misread as risk ratios: when the outcome is common, the odds ratio is much larger than the relative risk. Compute both, with intervals, using the Relative Risk Calculator.
Example
If 40 of 100 exposed people and 20 of 100 unexposed people have the outcome, the odds are 40/60 and 20/80, so the odds ratio is 2.667 although the relative risk is 2.0.