Cunning does not earn you any points at the end of the game. However, it can be used to your advantage in two ways. First, looking at the top of the card, you may blemish another players character by forcing them to discard a card they have played, in this case beauty. This causes the rival character to lose points, but also might affect which Suitors are interested them. If you want a particular Suitor to yourself, this could be a good strategic move.
The other way you can use Cunning is to play it on yourself, facedown. The Character who has acquired the most Cunning points at the end of the Courtship Stage of the game, will be the first character to roll for to see which Suitor proposes in the Proposal stage. This is a huge advantage, since there will be fewer Suitors available as the Proposal stage goes on.