Odds Ratio
An odds ratio compares the odds of an outcome in one situation to the odds in another. In logistic regression you get it by exponentiating a coefficient: an odds ratio of 2 means a one-unit increase in that predictor doubles the odds of the outcome, while 1 means no effect and below 1 means the odds shrink.
It is the everyday language for reporting logistic results because it is more graspable than log-odds. But beware the common slip of treating an odds ratio as a relative risk: doubling the odds is not the same as doubling the probability, and the two diverge sharply when the outcome is common (say already 40% likely).
If smokers have odds 4-to-1 of a cough and non-smokers 1-to-1, the odds ratio is 4 — but that is not the same as saying smokers are 4× as likely to cough.