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.

Typically propensity scores are modelled by taking pre-treatment covariates and including them in a model that predicts the probability of receiving the given treatment (most frequently this is done by fitting a logistic regression function that predicts treatment assignment to pre-treatment covariates, but other methods exist too like boosted regression and other machine learning methods).  So in that sense, the predicted probability or propensity scores is a single number that is created from a function of the pre-treatment covariates ("all the matching variables," as you say).  However, assessing balance is an entirely different endeavor.  To assess balance, one must examine whether significant differences in the distributions of covariates still exist after adjusting for the propensity score.
You'll find this reference to be a quick read that describes covariate balance and propensity scores in greater detail:  https://cran.r-project.org/web/packages/MatchIt/vignettes/assessing-balance.html
