This is a replica of Charles Babbage's first machine, circa 1833. This machine kept 32 decimal places, and was intended to generate tables of eighth order polynomials.
It was not the first mechanical calculator: machines that could multiply and divide were built as early as 1623. Nor was it the last. That honor belongs to the Harvard-IBM Mark I, completed in 1944. It kept 23 decimal places, had a memory of 72 counters, and could do a multiply in six seconds. (It had three units for calculating logarithms, exponentials, and sines.) The program could not branch or loop, since it was read sequentially from a paper tape.
The Harvard Mark II (and the Bell Relay Computer) used electrical relays instead. A relay is essentially an electric switch that can be closed or opened by electricity. They seemed like a good choice, since telephone exchanges were built from relays. Unfortunately, the Mark II wasn't much faster than the Mark I, and relays proved to be even less reliable than vacuum tubes.