Private campaigns enable you to create campaigns that won't appear in the marketplace. Only you and the influencers you pitch will know of their existence.
In order to make your campaign private, be sure to check the "I don't want this to appear in public marketplace" option within the Edit Campaign screen. You can change this preference at any time.
Private campaigns are only available with certain plans, so you may need to change your plan in order to unlock this ability. You can upgrade your plan at any time by clicking Change Plan under the Plan Information section within your brand account.