When two radio amateurs contact it is called a QSO. If they agree they can formally acknowledge this contact. It is this acknowledgement that is a QSL. This is done usually after talking to each other and agreeing to QSL.
The QSL is sent to the other station in the form of a card. They can do this via their local QSL Bureau. The RSGB for instance offers a QSL card forwarding service. If this can't be done then they can be send directly via the the real mail system.
The QSL cards themselves are about the size of regular postcard and have to be made of card. The station (i.e. the sender) puts their callsign on the top left of the card. As this is an acknowledgement of contact it will include details about that contact. This can include date, time, frequency, mode of transmission, and signal report. The card can also contain the stations QTH (location), the operators name, postal address and sometimes what equipment they use on their station.
Some people collect QSL cards that are from a far away country and others collect them for competitions. Others just want to remember a good QSO.