QSLs are paper postcards with call-letters on one side. They are sent from one radio ham to another to "confirm" the contact. QSLs are used to verify the contacts required for awards, as well as for display. Examples of awards are:
WAS = Worked All States, and DXCC = worked 100 different countries.
From the beginning of ham radio, QSLs were posted on walls, bulletin boards, and under glass. In recent years, the interest for paper QSLs has dropped off a bit as a result of eQSL and LoTW, but for many old-timers who loved receiving the cards through the mail from exotic places, that interest has never dropped off. Dan, N1ZZ claims he has over 10,000 QSLs in boxes. I believe it. There are now 340 countries on the DXCC list. Dan is the only person I know who has confirmations from 339. He is only missing one: North Korea where there are effectively no licensed hams.
I will always have a QSL ready for another ham, old or new. If you work me, I'll send you a card to confirm our QSO. That's how and why it's done.
Sometime soon, I will start scanning a bunch of QSLs I have received over my ham career. Several interesting ones I've received that come to mind: Ulaanbaatar Mongolia, McMurdo Station Antarctica, and Jonestown (Jim Jones) before the coolaid incident at Guyana, South America. Right now, I just have mine on this page because I already had these images in my computer memory. Check back.