"I've got Morgana again and I've got about six of her ... do you want it? You can start collecting."
-- Ron Weasley (PS6)
Chocolate Frog cards come in Chocolate Frogs candy (along with a chocolate frog). Hogwarts students collect and trade them. The faces on some of the cards are famous even to Muggles, although their magical abilities were not always recognized by the non-magical community.
Harry discovered Chocolate Frog cards during his first journey on the Hogwarts Express. In fact, he learned about Nicolas Flamel from the Dumbledore card he got then, and only remembered it later when he gave a Chocolate Frog to Neville to cheer him up (PS13).
Hermione gave Harry a large box of Chocolate Frogs for Christmas his first year (PS12) and he received Chocolate Frogs as get well presents after he defeated Quirrell (PS17). Hagrid gave Harry Chocolate Frogs for Christmas in his fourth year (GF23). Ron got Chocolate Frogs for Christmas in his fifth year (OP23) and in the Hospital Wing after he was injured in the Battle of the Department of Mysteries (OP38).
Lupin gave Harry the frog part of the Chocolate Frogs to help him recover during anti-Dementor lessons (PA12)
Students at Hogwarts collect and trade the cards. Hannah Abbott and Ernie Macmillan were swapping cards in the Three Broosticks (GF19). Harry, Ginny, and Neville were trading them on the Hogwarts Express (OP10). Notices about who wants which card even appear on the Gryffindor notice-board, in the common room (OP17).
When Dumbledore was being discredited by the Ministry of Magic, he was removed from the Wizengamot and from the International Confederation of Wizards. He told Bill Weasley that he didn't care what they did to him, as long as they didn't take him off Chocolate Frog cards (OP5).