In Coup, you want to be the last player with influence in the game, with influence being represented by your starting two face-down character cards in your playing area. The fifteen card deck consists of three copies of five different characters, each with a unique set of powers. On your turn, you take either a basic action (available to everyone) or a character specific action. These forms of actions as well as actions that are declared defensively in response to someone else, automatically succeeds unless the action is challenged.
Why would the action be challenged you ask? WELL: Since all character cards are face-down, any player can potentially take any action. And that's when it gets really interesting. Players are either lying or telling the truth when they take their actions, and that's where challenge comes in. If a character-specific action you take get's challenged, the player who took the action must reveal the character corresponding to the action. If they were lying, they lose one of their characters BUT if they were telling the truth, the player reveals his character, the challenging player loses one of their characters, then the challenged player shuffles his character in and draws a new one and play continues. The last player to still have influence – that is, a face-down character – wins the game!