While linear regression will predict an actual outcome for the dependent variable, logistic regression does not predict actual outcomes or events. What it will predict is the likelihood, (or odds ratio) of one of the events occurring. This is slightly different since it is related to the probability of an event occurrence (rather than the prediction of the event itself).
The odds ratio is defined as the ratio of the probability of an event A occurring divided by the probability of an event not occurring. In functional form, this ratio is expressed as a natural logarithm: