This is a replica made from one of Charles Babbage's designs. Although his government grants began in 1823, a fully working machine did not exist until 1853. (And at that, the working machine was built, in two years, by someone else.)
This machine worked to 32 decimal places, and was intended to solve eighth order polynomials. The British Navy, in particular, was interested in using it to compute navigation tables.
The values entered (as mechanical settings) were: the initial x, the initial y, the x-step, and the nine coefficients of the polynomial. By turning the crank, you caused differences (in the calculus sense) to accumulate, so that each "step" computed a new y. Babbage got his prototype to run at 44 steps per minute. In practice, the bottleneck was the speed with which a human could write down the results.