Finite Difference of Polynomial Functions..

My book is talking about 1st, 2nd and 3rd difference of a function with nowhere an explanation what it means. I've tried to Google it, but nothing relevant comes up.

It's asking me to find the 3rd difference for equation:

Then the next pages shows a table, with values between -3 and 3 for x, and values for f(x). The next column is 1st differences, then 2nd differences, and finally 3rd differences.

It looks like you just subtract the values from one column to get the result for the next column?

Then it is expecting me to know what the 3rd difference result should be by looking at the equation..Huh?