This charming contraption is described a "mechanical universal Turing machine". According the all-knowing Wikipedia:
A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer.
Here is a presentation by the maker, Jim MacArthur, describing the background of the machine. I gather the catch with this machine is that you have to assume that the length of track is infinite.
The machine was made mostly out of scrap metal and wood. The components include magnets, springs, cams and levers. It uses ball bearings as its memory. No electrical components were used, other than one small motor used to drive it.
[ Thanks Christoph! ]