A little bit of background for the paper and a brief summary might be beneficial:

The author is Alvy Ray Smith. He's one of the pioneers of computer graphics (http://en.wikipedia.org1/wiki/Alvy_Ray_Smith).

As the author states in the introduction: "If you find yourself thinking that a pixel is a little square, please read this paper."

To get from the point to the squares -interpretation you need to read a little bit forwards:

"Sampling Theorem tells us that we can reconstruct a continuous entity from such a discrete entity using an appropriate reconstruction filter"

This might be proper background reading before or after reading the paper:

http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_samplin...