Logistic regression is a statistical model used when the dependent variable is categorical. It models the probability of an event occurring through a linear combination of independent variables. There are three main types: binary logistic regression for two outcomes like spam/not spam; multinomial logistic regression for multiple unordered categories like food preferences; and ordinal logistic regression for ordered categories like movie ratings. Logistic regression estimates the parameters or coefficients of the logistic model using a maximum likelihood method.