The Kaplan-Meier (or product-limit) estimator turns the chain rule of probability into an estimator: survival past time t is a product of one-period conditional survivals, and each factor is estimated as the fraction of the currently observable population that survived that period. Censored observations contribute to every factor while they are visible, then exit the risk set without distorting later factors.
The output is a step function that drops at each observed event time, usually drawn with a Greenwood-formula confidence band. It has no covariates and no ability to extrapolate past the largest observed duration; segment comparisons are done by stratifying and testing with the log-rank test, and richer modelling hands over to Cox proportional hazards or parametric survival models.