One should increase the number of k-points to see how the physical quantity of interest (e.g., optical spectrum) changes upon increasing the k-mesh density. Note that one needs to substantially increase the density, e.g., not just using 5x5x5 instead of 4x4x4. Otherwise, you may not see much of a difference.
This kind of convergence tests are usually done for several different meshes. "Substantially" and the amount of testing effort are vaguely-defined things indeed, but this is where one needs to experiment to get reliable computational results within the tolerance you think is good enough for the problem of your study.
A good initial guess for k-point sampling usually comes with experience in doing calculations for different physical systems and quantities. The convergence speed with respect to k-point sampling can differ significantly for different physical quantities as well as physical systems (e.g., metals vs semiconductors).
