Short answers, pulled from the story.
A metalworking shaper moves a cutter riding on a ram that travels relative to a stationary workpiece. The ram reciprocates back and forth over the material during operation while cutting takes place only during the forward stroke.
Samuel Bentham developed a shaper between 1791 and 1793 during early industrial experiments. Roe credits James Nasmyth with the invention of the shaper in 1836 according to historical records.
Shapers were very common in industrial production from the mid-19th century through the mid-20th century. In current industrial practice shapers have been largely superseded by other machine tools including milling machines.
Jobbing shops and repair shops favor them because alternative methods are cost- or tooling-intensive. Tooling for them is minimal and very cheap to reproduce compared to modern alternatives.
Vertical shapers are generally fitted with a rotary table to enable curved surfaces to be machined. A true vertical shaper allows its slide to move from the vertical plane unlike a fixed slotter.