This is about how array operations in matlab work. In matlab, you can write things such as
>> [1 2 3] + 1
ans = [2 3 4]
In this case, the operation `+ 1` is applied in all columns of the array. In this exact manner, when you add a (1 x m) row and a (n x 1) column vector, you add the column to each row element (or you can view it the other way around). So the result is as if you repeat your (n x 1) column m times horizontally, giving you a (n x m) matrix, do the same for the row vertically n times giving you another (n x m) matrix, and then you add these two matrices. So basically adding a row and a column is essentially a shortcut for repeating adding these two (n x m) matrices (and runs faster than actually creating these matrices). This gives a matrix where each column is the old column plus the row element for that row index. For example
>> [1 2 3] + [1; 2; 3]
ans = [2 3 4
3 4 5
4 5 6]
A very practical example is, as I mentioned, getting all differences between the elements of a time series by writing `S - S'`. Another example, `(1:6)+(1:6)'` gives you the sums for all possible combinations when rolling 2 6-sided dice.
This does not work only with addition and subtraction, but with dot-product and other functions as well. You can do this across arbitrary dimensions, as long as your input matrices non-unit dimensions do not overlap.