In this usage of "map", the intended meaning is to determine the relation between cardinalities. To quote the dictionary sitting next to me, cardinality is "the number of elements in a given mathematical set." Combine the two and we have "determine the relation between the number of elements in either set." This is exactly what we are striving for. Since this is a phrase often used when talking about relational databases, it is safe to asssume that the intent is to define legal ways for tables to relate to one another.

One common mistake made by mathematicians and even other computer scientists is in mistaking the terminology of one discipline for another. For example, most biologists don't barge into a lecture on data structures and insist that the term tree isn't accurate, since it's upside down. And even if it was turned right side up, the root would extend further and branch out, not to mention a plethora of other simplifications. There are two reasons they don't do this. One, biologists and computer scientists are usually not crammed into the same room for extended periods of time. Two, they realize that any given group of academics will develop their own 'dialect' that is only meaningful to other academics in the same discipline.

In closing, I would like to apologize to Georg Cantor and rp for ever having used "cardinality" to describe the size of a finite set.