How does chessboard configuration affect camera calibration?
Generally speaking, when you are estimating a model from data, the more (independent) data points, the better the estimation.

In this particular case, the goal is to get as many 3d -> 2d point correspondences as possible, filling as much as possible of the volume of space of interest that is observed by the camera. The size of the squares directly affects how many data points you get per image (larger squares implies less visible corners/points). 

It is also important to ensure that the camera parameters you want to calibrate are observable given the data. For example, in order to calibrate the focal length (or the field of view, equivalently) you need to observe a significant perspective foreshortening of the (planar) checkerboard in a few images. In order to accurately calibrate the nonlinear (e.g. barrel) lens distortion, you'll need to observe plenty of aligned data points near the edge of the image, where the distortion is larger.

There is a longer response on StackOverflow that you may want to look up.