The Mediation app works by letting your own ad network accounts compete on Ezoic traffic against Google's Ad Exchange and Ezoic's other ad partners for the ad inventory on your site. Whoever is willing to pay the most wins the impression, ensuring that you're paid the highest amount possible.
On the Ezoic dashboard, you'll see the 'Mediation Ad Partner' earnings reported. Money collected through Mediation will be paid by Google to your own account and be reported in Ezoic as 'mediation earnings'. Any other earnings on your traffic going to your original site are handled separately from Ezoic.