The iPhone's iOS operating system is tightly controlled by Apple, as are the applications you find on the official Apple Store. Because of this, some users elect to "jailbreak" their iPhones to open the phone up to more customization, unapproved third-party apps and the ability to tweak otherwise unchangeable iOS settings. If you purchase a used iPhone for work and are not sure as to whether it has been jailbroken, you can find out with a few quick taps.
Look through the iPhone's apps and check for the normal installed apps. Apple's iPhone comes with several apps that can only be deleted through jailbreaking -- if any are missing, your phone is jailbroken. The default, un-removable apps are Camera, Photos, Music, Clock, Settings, Messages, Phone, Mail, Safari, App Store, Weather, Reminders, Calculator, Calendar, iTunes, Newsstand, Videos, Compass, Game Center, Contacts, Stocks, Voice Memos, Notes, Passbook and Maps.
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Search the iPhone for "Cydia." Thought this application can be hidden by clever jailbreakers, it is present on almost all jailbroken iPhones as it gives access to Cydia apps.
Connect your iPhone to your computer and use the iTunes "Restore" functionality. Once the restore process is complete, you can be certain your phone is not jailbroken.