A broken card is a card that is claimed to be too good to be used and can unbalance a game ... sometimes even "breaking" it to a point where the game can no longer be fun. Sometimes its a combination of cards that can break the game for example the character Luis Sera + the action card "A gift?" (Well in the hands of a talented player) can potentially break a game. Certain characters can become Broken simply by leveling up (I'm looking you Nightmare Ada Wong and Alliance Jack Krauser). There are plenty of cards in the game that can be considered broken... its just a matter of opinion ... (God thinking of what alliance Claire can do with GF and both herbs out is so stupid lol)
Edit* here's a list of cards I personally think are broken or have the potential to be
CHARACTERS - Ada Wong (N), Jack Krauser (A), Hunk (A), Luis Sera (N), Leon Kennedy (N)
WEAPONS - Flamethrower, Gatling Gun, Automatic Shotgun, Punisher, Silver Ghost, Samurai Edge
ACTIONS - A Gift?, Gathering Forces, Mind Control, High Value Targets, Lonewolf, Great Ambition
THE MANSION? - Those 2 **** Hunters from the nightmare set ... they need to die in a fire
These cards are some of the more "broken" cards in the deck. Some of the cards mentioned do however need other cards working together to become broken but on their own they're still pretty good.