First up, even though they have a lot of similarities, Coup isn't The Resistance. The Resistance is a team based game where you are trying to deduce who is on your team. In Coup, each player stands alone, holding two characters, and is trying to kill all other players at the table.
The twist in Coup is that the characters each player has are kept secret, and these characters allow for certain special abilities. On your turn you can claim to be any character that you like and use their special ability - to get money, change cards, or kill someone, for instance. As long as you are convincing, then cool, go right ahead. But if a player calls you out and is correct in their accusation, you'll have one of your own character's killed. If their accusation is incorrect, then they lose a character instead.
Your life is measured by the two characters you hold, so any kind of accusation or assassination has serious ramifications - you can only screw up twice!
And that's basically the game. We go around the table, claim to have a certain character in our hand, and take the effects of that character. In the meantime, players are trying to spot the liars, so they can call other players out and cost those players a life. And if a player can amass enough money, they can launch a coup - immediately killing another player's character with no chance of defense.
The complexity and fun comes out of the interactions between the characters. Some characters can counter another character's action, so without having to call someone a liar, you can stop them for performing their action. And the blatant lies and evasion also create a lot of good humour around the table - when a fourth person in the row claims to be the Duke and claim three credits - despite their only being three Duke cards in the deck. Or when someone keeps claiming that they are Captain, to block the Duke's actions, only to reveal on their turn that they are in fact an assassin.
So for the most part, Coup is a really elegant and often fun game, with lots of deception and player interaction. But you know… I actually don't like it very much! Maybe it's because I'm a bad liar.
The game is really quite lame the first time you play it - there are a lot of character interactions that don't make much sense, and unless you have a good understanding of them, you'll have a hard time bluffing. It may sound like I'm nit-picking, but I'm promise I'm not. I found those early games of Coup to be supremely painful. I've heard the same complaint from other players too - so I totally wouldn't use this as a gateway game for new players or with impatient players.
Next up, I really don't like how the Assassin character works. If you have three credits, you can assassinate another character - ok, that makes sense - and that character has a choice: they can call you out as a liar, accept the assassination, or claim they have the character that counters assassinations. If they call you out and you are not a liar, then they lose both of their characters (one for the assassination and one for the wrong accusation) and they're eliminated from the game. If they lie and say they can counter the assassination, and get called out in turn, again they lose both characters and are eliminated from the game. You can get eliminated from the game in one swift move. That feeling suuuucks! The only real way to counter the whole thing is to be really comfortable and confident with the game, so that you can counter earlier moves, preventing another player from getting enough credits to assassinate.
But then what's the point in calling another player whose actions are not yet effecting you, when if you call them out incorrectly you will lose a life?
But maybe that's just me. I'm terrible at Coup and so I always leave it thinking, "damn, this is boring." I can still understand that it is really elegant, swift, and has a lot going for it. Subsequently, a lot of my friends love it, but it really isn't for me. I think there are better bluffing games out there. The Resistance is one, thought for this niche of small and quick plays, I would personally recommend Good Cop, Bad Cop.