In iPhone 4 settings what does badge app Icon mean?

What happens when you turn this on?

The badge app icon is used to notify you of any updates or whatever needed in that application. For example when you need to update an app a small red circle appears on the top right of the app store app, indicating the number of apps needing updating. On the phone app, the same red circle indicates a missed call. That red circle is called the badge.

Hope that helps!

Its like when you get mail & there's a number in a red circle, that's the badge it is referring to.