Logistic regression is the technique of finding relationships between a set of input variables and an output variable (just like any regression), but the output variable, in this case, would be a binary outcome (think of 0/1 or yes/no).
For example: Will there be a traffic jam in a certain location in Bangalore? is a binary variable. The output is a categorical yes or no.
The probability of occurrence of a traffic jam can be dependent on such attributes as weather conditions, day of the week and month, time of day, number of vehicles, etc.
Using logistic regression, we can find the best-fitting model that explains the relationship between independent attributes and traffic jam occurrence rates and predict the probability of jam occurrence.