Brooches take many forms but a common shape is the disk or circle. It is actually one of the oldest shapes and was worn by Romans in the 1st to 4th centuries, and by the Franks and the early Anglo Saxons in the 5th and 6th centuries. Some of the Roman brooches were domed while those of the 5th century were saucer brooches, round disks with and up-turned brim, and others were flat round disks with enamel panels. Round brooches, heavily ornamented, were popular in the Byzantium period up until the 10th century. Round brooches with domed middles were worn in the 10th and 11th centuries by Vikings, particularly in Norway and Finland.
Round or discoidal brooches remained popular from the 15th century onwards although the way the brooch was decorated varied a lot. It might have enamel, set with gems, or be embossed.
I am not sure when round brooches with domed or decorated middles came to be called ‘target’ brooches but it is easy to understand how the name arose. Targets for use with bows and arrows, then guns and finally games had central ‘bull’s eye’ sections, with radiating concentric circles. They originated from cross-sectioned tree trunks. The term was certainly an understood description in the Victorian era, particularly from the 1860s onwards. There are quite a few target brooches from this period, set with garnet or agate cabochons, or with a star motif often set in the middle of an enamel or turquoise bead dome. Certainly, many target brooches copied the style of jewellery being excavated in the 19th century, such as Etruscan and Viking sites.