By default, your campaign will appear in the public marketplace unless you are subscribed to a Marketplace Pro plan or higher. If you are, you have the ability to set your campaign to private so it doesn't appear in the public marketplace.
This enables you to pitch influencers individually, rather than waiting for them to apply to be a part of your campaign. You can always upgrade your plan to unlock this ability.
If you are are subscribed to an eligible plan and want to set your campaign to private, select “I don’t want this to appear in the public marketplace” when creating or editing a campaign.
You can always change the visibility of a campaign by clicking Campaigns on the left sidebar then clicking the pen icon that corresponds with the campaign then select or unselect “I don’t want this to appear in the public marketplace” based on your preferences.