Logistic regression predicts the probability that a binary outcome occurs by passing a weighted sum of features through the sigmoid function. The model is linear in log-odds space, which is where its coefficients have their additive meaning; exponentiating a coefficient gives an odds ratio.
Despite its simplicity it remains a strong baseline for classification: it fits fast, its probabilities are well calibrated when its assumptions hold, and its coefficients double as evidence about which features matter. Its main practical hazards are separation (perfectly predictive features send coefficients to infinity) and nonlinear effects it cannot see without engineered features.