The size of the board you should use depends on the distance to the camera. Ideally, you want to place the checkerboard at the same distance from the camera at which you want to do your measurements. At the same time you want to have enough data points to cover your field of view.
If your checkerboard is too small, then you have two problems. First, at a large distance, you may not even be able to resolve the corners of the squares. Second, even if you can resolve the corners, the board will only cover a small part of the field of view in each image, so you would need many more images.
So, if you want to measure things a meter or two away, then an A4 board is sufficient. But if you want to measure things 10 meters away, then you want to use a much larger board with larger squares. And if you want to measure things kilometers away, then you just have to use the largest checkerboard you can find. :)
Here's a more detialed answer.