Propensity score gives the probability of a subject in a population to belong to a group of interest such as a treatment group.
Then comparing subjects with the same propensity scores across treatment and no-treatment groups enables the researcher to infer on the effect of the treatment regarding a given outcome even if he works on merely observational data.
But the researcher must beware of the unobserved differences between the group of interest and the comparison group created using the propensity score.
As always the relevance of the model depends on the nature of the covariates entered in it.
Garrido, M. M., Kelley, A. S., Paris, J., Roza, K., Meier, D. E., Morrison, R. S. and Aldridge, M. D. (2014), Methods for Constructing and Assessing Propensity Scores. Health Services Research. doi: 10.1111/1475-6773.12182