What is the relationship between the magic constant (the sum of each row) and the sum of all the numbers in the square? Why does this relationship make sense?

Let's say each row sums to 15

If we had 3 rows, then the total sum would be 3*15 = 45

If we added all of the values in the 3x3 magic square, then we'd get 45 as well.

This is one example showing that

sum of all values = (number of rows)*(magic constant)

You can replace "rows" with columns to get the same idea, because each column also adds to the same magic constant. The diagonals are an exception since we only have two of them.