To my experience it is the same as in other types of software, meaning the dividing of a model in basic blocks or structures that are small and simple enough to do calculations on them. Where finite element analysis used to be a separate software it is now built into most CAD software. So CAD meshes the model in order to use analysis tools.
To add, I would like to give the technical definition of it.
"Mesh Generation is the discretization of a given domain into simpler elements such as triangles or quadrilaterals (2D) and tetrahedra or hexahedra (3D)."
Meshing in a CAD system can have three meanings, namely triangularisation of a model to export it to other packages (render package, animation, ...), discretisation of a model into elements suitable for a FEM package, meshing of u- and v-parameter isocurves to let the user check the quality of a surface visually.
An example of the first is e.g. generation of an STL file.
An example of the second is e.g. generation of mesh file with tetrahedrals.
I have attached a screenshot of the three use cases.
This is a very loaded question. It depends on a lot of things, a limited answer has been given above by others.
First define the physical applicability of your domain:
Consider what is it that you mean by CAD, would a unified multiphysics based application qualify as CAD, would you have chemical behavior as well? Is there fluid in your CAD and or if there is magnetic flux, atomic level, fiber composites or myriad of other phenomenon, or is it just for geometric visual representation.
Assuming that you are only talking about amorphous solids, or Newtonian fluids, in your CAD model, isotropic materials. Perhaps you can simplify that even further by just looking at the geometrical grid. Now if its just the geometrical grid, maybe you have a fourth dimension, "time" which will be an interesting aspect to model. You can add further dimensions to your grid, such as chemical reactivity with sources that vary in dimension and space in each of your grid elements. There are many other meshes that are not mentioned above, such as polyhedral meshes, For all these there will be a specific grid/mesh that will be most appropriate...
Why create a mesh what is its use: All meshes are used to discretize your domain into a simpler domain where the governing equations of your materia-domain can be significantly simplified within your acceptable level of error. If that would happen with linear elements or plane elements or 3d elements that will depend on application, applicability and the physics being modeled. It could just be for geometric representation...
Thus there is no simple answer to such a loaded question in a wide field of mathematical modeling.