A marketplace application is when an influencer applies to be a part of your campaign if you have made it open to the public.
If you want to receive marketplace applications, be sure that the "I don't want this to appear in public marketplace" is unchecked in the Edit Campaign screen. You can change this preference at any time.
The number of marketplace applications you can receive is determined by your plan tier. You can upgrade your plan at any time by clicking Change Plan under the Plan Information section within your brand account.