Go to settings, more, about device, tap on build version 7 times and go back to more (settings main screen) and you should now see the developer option...
Its used for a lot of different things, contact transfer for one with certain devices with debugging on and stay on, developer options also allows for quick access to the device from a PC via ADB. Developers find this useful, as it allows them to quickly deploy their app and debug it. The feature is indispensable to Android hackers and enthusiasts as a means to quickly access and control their device from the PC. Several guides, hacks, and mods for Android devices posted here at XDA involve significant use of ADB commands