We have investigated the origins of large orbital magnetic moment (OM) and unique magnetic anisotropy in the quasi-1D magnetic cobaltate, $\ensuremath{\alpha}$-CoV${}_{2}$O${}_{6}$, employing both the ab initio band structure method and the microscopic cluster model calculations. We have found that the peculiar crystal electric field effect in $\ensuremath{\alpha}$-CoV${}_{2}$O${}_{6}$ combined with the strong spin-orbit coupling induces the unusually large OM and other intriguing magnetic properties of $\ensuremath{\alpha}$-CoV${}_{2}$O${}_{6}$. The observed 1/3 magnetization plateau in the $M$-$H$ curve is explained by the spin-flip mechanism based on the MC simulation. Anomalous magnetic entropy behavior is attributed to the strong uniaxial magnetic anisotropy in the quasi-1D Ising chain system.