Hello,
Each time you have checked an app or apps it will sync from your device into itunes or vice versa. Not synced, the apps will not be on your device but stays in itunes. The apps are stored in the mobile applications folder (user/music/itunes/itunes media/mobile applications). If you decide to delete an app or two, it will be removed from the mobile applications folder. But you can always log in back into your itunes account and redownload those apps. The apps downloaded uses your Apple ID. Hope this answers your question.