"Optimization Goal" defines what actions you want the campaign to be optimized towards. Facebook uses this optimization goal to decide to whom to show your ads inside your target audience. For example, you can choose "App Installs" as "Optimization Goal" to have the ad shown to the users who are more likely to install your app. You also bid for the optimization goal. If your optimization goal is app install and your bid amount is 5 USD, then you are saying Facebook that you are willing to pay 5 USD at most for an app install.
"Billing Event (Pay Per)" defines how you are going to be charged when your campaign wins an auction. The most common billing event is impressions but, depending on the campaign objective and optimization, can sometimes be customized, for example to link clicks or app installs. If you select "App installs" as your "Billing Event", then you will be charged every time a user installs the app.