Offer Access allows you to set the restrictions to your offer.
Public: By default, offer would be public and all the affiliates would be able to access and send traffic to this offer.
Required Approval: This option is for affiliates wherein they have to get the offer approved before pushing the traffic for the offer.
Private: This option allows you to make an offer private that hides the offer from other affiliates and allows you to grant the access to selected affiliates.