Camera calibration using multiple images
You are correct: to calibrate a camera you need a correspondence between 3D world points and 2D image points. The problem is that the 3D points cannot be co-planar, so people were building 3D calibration rigs, e. g. a box made of checkerboards. One image of a rig like that would be enough to calibrate, but those rigs are hard to build, because you have to get the planes to be at exactly right angles to each other. 

Then Zhengyou Zhang came up with the algorithm to calibrate from multiple images of a planar pattern, like a checkeboard. You still need non-coplanar points, but you get them from multiple images of a planar pattern in different 3D orientations, rather than a single image of a 3D rig.

Noise and errors are another reason why you need multiple images. You cannot detect the checkerboard corners with infinite precision. So you need a lot of points, to estimate the camera parameters more reliably.