Advertisement -- this is a noun, sometimes shortened to "ad".
(There are many advertisements on TV.)
Advertising -- this can be used as a verb or a noun (and an adjective?). As a verb, it means to advertise.
(Many English teaching companies were advertising during the Olympics.)
As a noun, it means advertisements generally.
(We don't plan to purchase any advertising this year.)
Like many nouns, it can also be used as an adjective -- (the advertising department of a company)
Hope that helps...