balance in propensity score I often hear many authors talk about how propensity score helps achieving balance or similarity between treatment groups. Propensity score collapsing information about all the matching variables into a single summary statistics that measures how much an observation resembles treatment observations on baseline characteristics etc...
I am not sure I understand this clearly. What does this mean ? "Propensity score collapsing information about all the matching variables into a single summary statistics"
What about the effect of covariates ? How is this estimated if Propensity score collapses information about all the matching variables into a single summary statistics.
Please pardon my ignorance. Need some help understanding this with some examples. Thanks in advance.

You have hit on some key questions.  By ignoring covariates except in how they relate to treatment choice, you are not accounting for outcome heterogeneity when doing propensity score analysis (if done the usual way).  This results in a great loss of power and biased estimation of treatment effects due to non-collapsibility of odds ratios etc.  Propensity scores are needed (for the pure confounding part of the analysis, not for the outcome heterogeneity part) when you require data reduction because of too small an effective sample size for the number of covariates to adjust for.  Propensities balance because of the following reasoning.  Suppose that accounting for a propensity to treat of 0.3 still resulted in an imbalanced age distribution between treatments.  That implies that age was mismodeled when specifying the propensity model.  If age were properly modeled, once adjusting for propensity age no longer predicts treatment choice.  But then the outcome heterogeneity problem rears its ugly head.
