Ham radio operators send QSL cards to each other as a way of verifying contact between stations. QSL is what's known as a Q code used in radio communication. As far as I know, it stands for Query Station Location. The cards would include the call signs of both stations as well as other information, including the date, time, mode of transmission, frequency and a signal report. Occasionally, they also include information on the equipment used. Although some cards are very simple, others are very creative and colorful, like this one.
This operator sent his card from Moscow, USSR in 1959.
The cards are sent in envelopes, either directly to the recipient or through QSL bureaus, which forward them on to recipients. Use of the QSL bureaus cuts down on postage costs, but delivery time is longer. Nowadays, people can also send the QSL cards electronically as .jpg files. While there is no postage cost with this, and the confirmation is very quick, it lacks the quality of a paper card that has traveled across the country or around the world.
Many ham radio operators have large collections of QSL cards. I think the hobby is not as widespread as it used to be though. Sadly, technology has diminished the role of the ham radio for communication in emergency situations as well as for recreation.
Here's a link to a website that highlights old QSL cards.