  The present authors introduced the notion of \emph{weakly unobstructed}
Lagrangian submanifolds and constructed their \emph{potential function}
$\mathfrak{PO}$ purely in terms of $A$-model data in [FOOO2]. In this paper, we
carry out explicit calculations involving $\mathfrak{PO}$ on toric manifolds
and study the relationship between this class of Lagrangian submanifolds with
the earlier work of Givental [Gi1] which advocates that quantum cohomology ring
is isomorphic to the Jacobian ring of a certain function, called the
Landau-Ginzburg superpotential. Combining this study with the results from
[FOOO2], we also apply the study to various examples to illustrate its
implications to symplectic topology of Lagrangian fibers of toric manifolds. In
particular we relate it to Hamiltonian displacement property of Lagrangian
fibers and to Entov-Polterovich's symplectic quasi-states.
