You can see what Wikipedia says here: http://en.wikipedia.org/wiki/House_of_Plantagenet There's a very brief history of the Plantagenets here: http://www.royalinsight.gov.uk/output/Page58.asp and there's a family tree here: http://www.royal.gov.uk/files/pdf/plantage.pdf

It is said that the name came from the planta genesta= a broom plant, that was reputedly worn by the sire of this line, Geoffrey of Anjou. However, this is disputed by many scholars, as the story seems to be a late one: The Plantagenet name is often incorrectly applied as though it were the surname of all (or many) of the English kings throughout the 350 years from Henry II to Richard III but contemporary evidence for its early use is sparse. As John Gillingham (2001) [John Gillingham, The Angevin Empire, Second Edition (London, 2001), p 3.] remarks: "But although Henry II's father Count Geoffrey was known as Plantagenet it was not until the fifteenth century that this term came to be used as a family name, and for the story that the name came from the sprig of broom (Planta Genista) that he liked to wear in his hat to be put into writing we have to wait until the nineteenth century." We may quibble about John Gillingham's statement that the `sprig of broom' story did not appear in print until the nineteenth century. This is in error for, in 1605, William Camden wrote of Plante Genest that he was so called because `he ware commonly a broom-stalk in his bonnet'. Even so, Gillingham is not alone in doubting this story -- 1605 is long after the first evidence in the 1170s for Geffrey's nickname. Rather than just as a fashion accessory for his hat, we might surmise that it is likely that the nickname Plante Genest was an echo of the earlier name Plantevelu. It is of course possible for both explanations to hold true: the name Plantegenest was an echo of Plantevelu and Geffrey Plante Genest reinforced that association by wearing a sprig of broom in his hat. The Encyclopedia Britannica (2000 version) makes similar points though it credits a different story of how Geffrey's nickname may have originated. "Although well established, the surname Plantagenet has little historical justification. It seems to have originated as a nickname for Count Geffrey and has been variously explained as referring to his practice of wearing a sprig of broom (Latin genista) in his hat or, more probably, to his habit of planting brooms to improve his hunting covers. It was not, however, a hereditary surname, and Geoffrey's descendants in England remained without one for more than 250 years, although surnames became universal outside the royal family. ... The first official use of the surname Plantagenet by any descendant of Count Geffrey occurred in 1460, when Richard, Duke of York, claimed the throne as ``Richard Plantaginet''." Hints of the hunting explanation for the name appear, in a less fanciful fashion, in the Complete Peerage [Complete Peerage, Volume XI Appendices, p.~141] which largely dismisses hunting in favour of Geffrey's liking for a `sprig of broom' in his hat. "Mrs Green says that Geoffrey was so called ``from his love of hunting over heath and broom'' (Henry II, p.~6). This may be deduced from Wace (loc.~cit,): E al contre Geffrei son frere, Que l'en clamont Plante Genest, Qui mult amout bois e forest. However, it is more likely that Geoffrey's love of wood and forest was inserted for the purpose of rime than as an explanation of his nickname." One might add that Geffrey was most famous for his marriage in 1128 to the heiress apparent to the English thone and for his conquest of Normandy in 1144. This may well have been more in the mind of the Norman poet Wace (1135-74) when he wrote his poem which can be taken to allude to Geffrey's love of increasing his lands like his predecessor Plantevelu. His augmentation by marriage and conquest can be taken to be evoked by the Plante Genest metaphor of a germinating shoot. When John of Marmoutier referred to Geffrey Plantegenest in the 1170s he was writing to please Plante Genest's son Henry II (nicknamed Fitz Empress) and, with the Plantegenest nickname, he may well have been alluding to Geffrey's gallantry. The Latin meaning of planta was a `shoot for propagation' and this had led on to the `hairy shoot' meaning of the ninth-century name Plantevelu in Aquitaine. Connotations of generation should be placed in the context of late medieval metaphysics rather than modern biology. Transubstantiation became an article of Christian faith in 1079 though it had been believed by many earlier. By the early thirteenth century, Western European scholastics were developing elaborate schemes for man's soul with its vegetable, animal and intellective components. Geffrey Plante Genest's nickname probably related to his powers of generating through marriage the shoots of an Empire, for he augmented by marriage his family's Angevin claims. Names of philandering were popular though, with the mid-thirteenth-century Savoyard connection, there may have been some interchange of influence between English and Swiss Plant-like names. English: Plantebene - pleasant shoot Plantefolie - wickedness shoot Planterose - risen shoot Swiss: Plantefoi - planted faith Plantamour - planted love Planteporrets - porrected shoot Plantefor - planted conscience With the Queen's uncle Boniface of Savoy as archbishop of Canterbury and his compatriot Peter of Aigueblanche as bishop of Hereford, the Savoyard influence may have been more godly than the `hairy shoot' tradition implied by such names as Plantevelu and Plantefolie. Those who knew scholastic teachings may have been aware of religious aspects to Plant-like names. Johannes Scotus Erigenea wrote in the ninth century that bone, nail and hair contained only insensitive vegetable life (cf. Plantevelu). Atto, bishop of Vercelli (924-61) complained of the practices of meretriculae in his diocese who baptised turves and branches as coparents. Avicenna (c980-1036) maintained that the soul of plants was shared with animals and humans. Averroes (1126-98) reiterated a scheme for the generation of life from the elements, such as clay, through plants and animals to man. Robert Grosseteste (c1175-1253) and others wrote significantly about the vegetable soul with its powers of nutrition, augmentation (cf. Planterose, Planteporrets) and generation (cf. Plantevelu, Plantegenest). The human soul had three components: vegetable; sensory; and intellective. Roger Bacon (c1214-c1294) said modern philosophers taught that only the intellective soul was directly created by God (cf. Plantefoi, Plantamour, Plantefor). As scholastic ideas became better known, a more developed metaphysical explanation for the Plantagenet name may have come more to the fore. By those times the English word plant was coming to mean more a grown shoot rather that just a shoot, and the word genet had animal-life sense as a civet cat or a horse. The civet cat is elongated and hairy -- this may be compared with the Swiss name Plantaporrets, associated with the elongated leek plant, as well as with the `hairy shoot' meaning of Plantevelu. The sprig of broom also is hairy. More generally, Plantagenet can be associated with transubstantiation through the vegetable (planta), animal (genet as a civet cat or horse) and human genera. In particular, the word {genet} means a small Spanish horse and the Plantagenet name may have come to evoke an image of the young Geffrey, as a scion or establisher shoot (planta), at one with his mount (genet) in 1128 in his pre-nuptial joustings at Rouen. By the mid-fifteenth century, Plantagenet had become a royal surname, relating to the renewal of the immediate male line, following the madness of the Lancastrian king, Henry VI who was replaced by a king from the rival House of York. The Plantagenet name embodied a sense of this creative renewal as well as indicating that the House of York descended, like that of Lancaster, from Geffrey Plante Genest, their common forefather of some three hundred years earlier. http://archiver.rootsweb.com/th/read/GEN-MEDIEVAL/2006-02/1139996934

THE Plantagenet Kings of England begin with Henry II., who became King in the year 1153, and end with Richard II. two hundred and forty-five years later. The father of Henry II. was the first to bear this name, and he received it because of his habit of wearing a sprig of the "broom" plant (planta genesta) in his cap.