This topic is explained at EAAccessoryManager Class Reference, on showBluetoothAccessoryPickerWithNameFilter:completion: that says that:
This method synchronously displays an alert containing the list of Bluetooth accessories that have been discovered by the current device and that match the specified filter (if any). The user can select an accessory from this list and pair the device to it. Pairing an accessory updates the accessory manager’s list of connected accessories and generates a corresponding connection notification.
Of course it's not enough to connect the external device successfully, because you have to do a few more steps before and after calling this method, like adding a protocol string of the external device on "Supported external accessory protocols" property of your project's plist etc, but it would be an answer to another question. Hope it helps.