Logistic regression is used with binary data when you want to model the probability that a specified outcome will occur. Specifically, it is aimed at estimating parameters a and b in the following model:
where pi is the probability of a success for given value xi of the explanatory variable X.
Use of the log of the odds p/(1-p) (the logit) guarantees that the predicted value of p will always be between 0 and 1.