Short answers, pulled from the story.
The Geats were a large North Germanic tribe who inhabited Götaland, meaning the land of the Geats, in what is now southern Sweden. They lived there from antiquity until the Late Middle Ages and are one of the founding peoples of modern Swedes, alongside the Swedes and the Gutes.
The earliest known surviving mention of the Geats appears in the work of Ptolemy in the 2nd century AD, where he calls them the Goutai. By the 6th century they are also mentioned by Jordanes, who calls them Gautigoths, and by Procopius, who calls them Gautoi.
The question is long debated and unresolved. Old Icelandic and Old English sources clearly separate the two groups, but the Gothic historian Jordanes wrote that the Goths came from the island of Scandza and named one of its tribes the Gautigoths, implying a connection. Archaeological evidence, including the appearance of Scandinavian burial customs in what is now northern Poland during the 1st century AD, also suggests a link.
Most scholars accept the identification. The Old English Gēatas is the regular phonological equivalent of Old Norse Gautar and modern Swedish Götar, and the poem places the Gēatas east of the Danes and in close contact with the Sweons, matching the historical position of the Geats in southern Sweden. Two minority hypotheses identify Beowulf's Geats with the Jutes or with the Gutes of Gotland.
The process was gradual and much debated. Papal letters from the 1080s still distinguished the king of the Swedes from the king of the West Geats, and Swedish kings only began styling themselves kings of the Geats in the 1270s. After the Kalmar Union in the 15th century, Swedes and Geats appear to have begun perceiving themselves as one nation.
The name Geat derives from a Proto-Germanic root *geutanan, meaning to pour. It shares this origin with the names Goth and Gute, all being ablaut grades of the same word. One interpretation is the figurative meaning they who pour their seed; another connects it to watercourses in the region, though that reading has not been widely accepted.
The title was removed in 1973 when Carl XVI Gustaf became king and decided his title should simply be King of Sweden. Until that point, the official title had included Kings of Sweden, the Geats and the Wends, a formula rendered in Latin as Suecorum, Gothorum et Vandalorum Rex.