You can't edit an existing board to make it secret. You can only create new secret boards.
Similarly, you can't edit a Pin and move it directly to a secret board. Since existing boards or Pins may already have Pins or likes, you can't make them secret.
If you'd like to make public content secret, you can add a Pin from a public board to a secret one. This creates a secret "copy" instead of changing the state of the original Pin. You can then delete the original Pins without affecting the secret Pins.