Central: A Bluetooth® device such as smart phone, tablet, or PC that initiates an outgoing connection request to an advertising peripheral device.

This Bluetooth module ties directly into the Tx and Rx lines of the Arduino so a wireless serial connection between an Android device can be established.

In Connecting to Intel® Edison from Android* with Bluetooth* LE (BLE) describes a way to access BT via Arduino code but additional BT shield/kit is required.

This lets you connect existing Arduino Shields to add Bluetooth, a touchscreen, or more for testing or hardware development purposes. via PRWeb Support Liliputing ...

The $22 kit includes an Arduino-BLE board and 6-pin header that should be fairly broadly applicable for building Arduino-based hardware that can communicate with iOS devices.