Gilday explained how the process works. The front-facing camera is employed to take pictures of each side of the cube, and starts working on a solution by using an algorithm. The engineer says that the quad-core processor and the 2GB of RAM combine to help solve the problem. A Bluetooth connection allows the phone to communicate with the Lego Mindstorms, which also has an ARM based processor inside.
For the record, with the Huawei Ascend P6 as its brain, the Lego Mindstorms solved the cube in just 49 moves.
source: ARM via AndroidAuthority