  Two-dimensional van der Waals magnetic materials are of great current
interest for their promising applications in spintronics. In this work, using
density functional theory calculations in combination with the maximally
localized Wannier functions method and the magnetic anisotropy analyses, we
study the electronic and magnetic properties of MnPSe$_3$ monolayer. Our
results show that it is a charge transfer antiferromagnetic (AF) insulator. For
this Mn$^{2+}$ $3d^5$ system, although it seems straightforward to explain the
AF ground state using the direct exchange, we find that the near 90$^\circ$
Mn-Se-Mn charge transfer type superexchange plays a dominant role in
stabilizing the AF ground state. Moreover, our results indicate that although
the shape anisotropy favors an out-of-plane spin orientation, the spin-orbit
coupling (SOC) leads to the experimentally observed in-plane spin orientation.
We prove that the actual dominant contribution to the magnetic anisotropy comes
from the second-order perturbation of the SOC, by analyzing its distribution
over the reciprocal space. Using the AF exchange and anisotropy parameters
obtained from our calculations, our Monte Carlo simulations give the N\'eel
temperature $T_{\rm N}=47$ K for MnPSe$_3$ monolayer, which agrees with the
experimental 40 K. Furthermore, our calculations show that under a uniaxial
tensile (compressive) strain, N\'eel vector would be parallel (perpendicular)
to the strain direction, which well reproduces the recent experiments. We also
predict that $T_{\rm N}$ would be increased by a compressive strain.
