Wat is Optimal stopping problem, Snell envelope?

Given an adapted, integrable reward process $(G_n)_{n\le N}$, the optimal stopping problem is to find $\sup_\tau\E[G_\tau]$ over stopping times $\tau \le N$. Its Snell envelope is defined backward by $U_N = G_N$ and $U_n = \max(G_n, \E_n[U_{n+1}])$.