Why is the pressure correction added in the Van der Waals equation?
You may consider the vdW equation as the deviation from the ideal gas state equation $pV_\mathrm{m} = RT$.

If you look at the vdW equation 

$$\left(P+\frac a{V_m^2}\right)(V_m-b)=R T$$

you can easily see why the corrections have  their signs.



The pressure term correction has the positive sign,
as the real gas has  due molecule cohesion  smaller volume than  an ideal gas at the same pressure. Like if it was under bigger pressure than it really was. 

Increasing $p$ term by a positive correction leads to lower predicted volume than for ideal gas, at the same pressure, because of cohesive force.

$$V_m=\frac {R T}{\left(P+\frac a{V_m^2}\right)}$$

The correction simulates this bigger pressure the ideal gas would need to get the same vol.



The volume term correction has the negative sign,
as the gas has at the given volume
higher pressure due molecule own volume.

Decreasing $V$ term by a negative correction leads to higher predicted pressure than for ideal gas, at the same pressure, because of own molecule volume.

$$P=\frac {R T}{(V_m-b)}$$