Odds re-express a probability as successes per failure: a probability of 0.75 is odds of 3 to 1. Logistic regression is linear in the log of the odds, so each coefficient adds to the log-odds, and exponentiating a coefficient gives the odds ratio: the factor by which one unit of that feature multiplies the odds.
An odds ratio of 1 means no effect, which makes it a natural feature-importance reading: effects with confidence intervals clear of 1 carry signal, while intervals straddling 1 flag features the data cannot distinguish from noise. Odds ratios are not probability ratios, and the difference grows as probabilities move away from small values.