A type of hard candy, AKA a bull's eye. These were a common type of penny candy in the early half of the 20th century. The flavoring would have been up to the candy maker and may have varied a fair amount, but the fact that they were referred to as Jackson balls rather than a more specific name indicates that they were fairly nondescript in flavor. While it is unclear if there was a definite difference between bull's eyes and Jackson balls, it appears that bull's eyes were expected to have a fairly distinct pattern of swirling, alternating colors, today most associated with mint candies, and that Jackson balls were not.
As a historical oddity, the name Jackson ball is most often referenced in regards to the devices for cutting them; this may be because bull's eyes required scissors to cut neatly without ruining the pattern, while cruder devices could be used to make Jackson balls. It might also be that Jackson balls were bigger, and therefore not easily cut with scissors. Regardless, Jackson ball cutters tend to be counter-top mounted pincers with long-levered handles, or multi-toothed rollers that look like miniature farm equipment, much sturdier than any scissors.