BLE Shield stands for Bluetooth Low Energy (BLE) Shield. It is designed to work with Arduino boards or compatibles, including Arduino Uno, Mega 2560, Leonardo and Due. It allows you to connect your Arduino boards with other BLE Central device like a smartphone or tablet. So you can develop some applications like:
BLE shield can operate under 3.3V or 5V, therefore it works with a lot of Arduino compatible boards.
Android 4.3 or above (4.4 recommended for stability) with Bluetooth 4.0 hardware support
Windows 8.1 with built-in Bluetooth 4.0 or USB dongle
Mac OSX 10.9.2 with built-in Bluetooth 4.0 or USB dongle
Linux with BlueZ 5.1 with built-in Bluetooth 4.0 or USB dongle