I refer to this paper but reproduce a simplified version of their argument. Apologies if I have misrepresented the argument of the paper!
Alice has a classical description of a quantum state $\rho$. Alice and Bob both agree on a two outcome observable $M$. Now, the goal for Bob is to come up with a classical description of a state $\sigma$ that gives the right measurement statistics i.e. $Tr(M\rho) \approx Tr(M\sigma)$.
The way this is done is that Bob has a guess state, say the maximally mixed state, $I$. Alice then tells him the value of $Tr(M\rho)$. Bob then measures the maximally mixed state repeatedly (or he runs a classical simulation of this with many copies of the maximally mixed state) and "postselects" the outcomes where he obtains $Tr(M\rho) \approx Tr(MI)$. In this way, he obtains a state that reproduces the measurement statistics of the true state.
What is the meaning of postselection in this context? How does Bob go from $I$ to $\sigma$ in this procedure?