Adafruit Bluefruit LE (Bluetooth Smart Bluetooth Low Energy Bluetooth 4.0) nRF8001 Breakout allows you to establish an easy to use wireless link between your Arduino and any compatible iOS or Android (4.3+) device. It works by simulating a UART device beneath the surface sending ASCII data back and forth between the devices letting you decide what data to send and what to do with it on either end of the connection.

Unlike classic Bluetooth BLE has no big contracts to sign and no major hoops that you have to jump through to create iOS peripherals that you can legally design and distribute in the App Store which makes it a great choice compared to classic Bluetooth which had (and still has) a lot of restrictions around it on the iOS platform.