Closed Geometry
 

I wanted to ask that what is exactly meant by closed volume or closed geometry? Say in a cad, there shouldn't be an empty space inside?

A better term is watertight. If you placed the geometry in a bucket of water would the interior remain dry or would you have a leak. A closed geometry is one that is watertight.

So all the extrusions and the lofts that are solid should be closed whereas the surfaces that are not convex would be open(or not closed) geometry, right!

I do not understand the concept why air interactions in softwares like Altair Virtual Wind Tunnel need a closed geometry. They should even be able to simulate the vortices or so in the real car right if it has a not-closed geometry!

Closed geometry is more of a requirement for the mesh generation. You only want mesh where you actually have flow, and unnatural surface concavities (such as between surface patches that don't match up perfectly) tend to break most meshers.