The probability of receiving a treatment given a set of observed covariates.
The term propensity-score comes from the literature on treatment evaluation. The word treatment has to be understood in a large sense. It can be a medical treatment, but it can also be the participation in a policy or a program, such as e.g. job training.
The propensity score is the probability that a subject receives a treatment given a set of observed covariates.
The propensity score is used to estimate the impact of a treatment, either via matching, weighting, or regression.