The term QSL is ham short-hand for Can you confirm?/I confirm.
When hams are using CW (continuous wave, or Morse code); instead of spelling out a lot of phrases they use the Q code.
Three letters all beginning with Q (Question) save a lot of time.
The reply is usually the same three letters. eg q: QTH? a: East Overshoe, NY.
The QSL cards are usually sent by both hams as a confirmation of their QSO (contact).
Often, the cards go to a central QSL bureau (something like a post office) where volunteers sort the cards for distribution.
The Australian (Cinderella) stamp is one applied at some bureaus to show it has been handled by that particular bureau.
Since many hams make thousands of contacts per year, the bureau system is a convenient money-saving way of sending out "confirmation of contact" cards.
The cards which have been sorted by the bureaus are bulk-shipped to and from bureaus in other countries; and, while it is cheaper than by regular mail, it can mean long delays (even several years) in getting a confirmation.
The cards may be needed quickly by a particular ham to verify a contact with a ham because the QSL is needed as proof for a ham who is trying to get some sort of an award for making contacts with certain countries or for making contact on particular frequencies.
In that case, sending cards directly or (in the past several years) by email is done.
Many hams are stamp collectors (myself included) probably because of our common interest in geography.