But first a bit of explanation. A Turing Machine is a sort of computer first proposed in 1936 by Alan Turning. This computer is a bit different from the modern computers we have today. All the instructions are "built-in" to the computer. It reads data from a "tape", processes it according to its built-in program, and writes a result. I should emphasize that the Turing Machine is (to my limited understanding) generally thought of as a conceptual model of a computer, not as a practical device. I doubt Alan Turing ever thought that someone might go and build such a device, much less that they might build it out of out of LEGOS! (Sigh ... anyone else remember when LEGOS were plastic bricks, instead of pre-packages toys with some assembly required?) For example, if the machine encounters two "1" bits (or maybe two consecutive LEGO blocks in the "up" position), its program might cause it to change the second bit to "0" (or moves the LEGO block to "down").
More information and some cool pictures can be found on the project blog: Lego of Doom.