There are two main types of rims commonly used nowadays, box-section rims (rectangular in cross-sections) and deep-section rims (triangular in cross-section).
For road race involving hill climbs, a stiff and lightweight rims with low rotational weight is essential to optimize the acceleration and climbing performance. However, if we race on a flat stage, it is the deep-section rim that will provide the aero dynamic advantage reducing drag forces.
It is crucial that riders choose the right depths of rims for different conditions and race situations.
The rim determine the stiffness of the wheel by its depth, its torsion strength and spoke length and a stiff and deep section rim will comes with shorter spokes that will make wheel laterally stiff.