I would really like to learn generating functions before I take my exam next week...

For example, how many ways can you make like $2.37 in pennies, nickels, dimes and quarters?

I kindof understand how to get the generating function (like (1/(1+x)) * (1/(1+x^5))*...

but what does it mean?

EDIT:

Also, thats the Kotch snowflake in the upper left hand corner is it not? A 4-d object if I remember correctly (or something like that)