The term 'received pronunciation' was first used in the early 1800s, with the unusual use of 'receive' to mean 'accept as true or authoritative', which we also meet in 'received wisdom'. In this sense we can talk about the received pronunciation in Edinburgh or California. However, the capitalized term Received Pronunciation was introduced by the
phonetician Daniel Jones in the early 1900s to refer to the particular accent which was then the mark of someone who had been educated in one of the great public schools in the south of England.
Since the public schools required money, and scads of it, to get into, working-class people did not get to learn the accent, so it was a marker of class. It is also not the native accent of any region of Britain, though it is associated with the cultural and economic dominance of the Home Counties of the south, including London and the universities of Oxford and Cambridge.
Its rise coincided with the high point of the British Empire, and it was strongly identified with the ruling class, and with privilege, education, and gentility. These days that is no longer wholly so, and it may be disparaged as posh, and lacking street cred. It is usually heard as an attractive accent too, though people outside British culture may rate regional accents as more attractive.
Daniel Jones described the phonetics of this accent when sound recording, broadcasting, and the science of phonetics itself were all new, particularly in his English Pronouncing Dictionary of 1917. RP, as it's widely known, became the first English accent to be comprehensively recorded and studied. It is traditionally the standard accent taught to foreigners. It is still a staple of linguistics textbooks, and it is still taught, though like all accents it has changed over the years, and the RP now spoken by some younger people is sometimes called things like neo-RP, Regional RP, or Advanced RP.
In recent years a new accent has spread, a modified RP combined with features of local London English. This intermediate accent, called Estuary English, is spreading across England, and some aspects have been reported in Scottish cities. Almost inevitably, RP will cease to be the standard accent, and Estuary (also known to linguists as EE) will take its place. See also my node changes in southern British pronunciation for an overview of the shifts in accent.
Phonetic features making the accent stand out from related varieties of English are mainly in the vowels. It shares with related accents the fact that wh is pronounced w (except for some older speakers), and that r is silent except before a vowel. Unlike most regional accents, h is always pronounced. Formerly the groups tu du were as if tyu dyu, not chu ju, at least when stressed; though these days most RP speakers make them chu ju everywhere.
The short vowel i as in sit is more widely used than in other accents: finally, as in city, when unstressed, as in indivisibility - both these words have all the same vowels -, and representing an unstressed e, as in regarded = rig-AAD-id.
The long back vowel aa as in father, park, calm, path was deeper in the throat. The short vowel u as in cut was an unusual sound, hard to describe, not quite a neutral vowel, and very rare in the world's languages. In the modern form of RP these two vowels have shifted and are now effectively the long and short forms of the same ah vowel.
eea and ooa as in deer, dour are diphthongs, whereas in related accents they may be disyllables DEE-ah, DOO-ah.
The ou diphthong as in go, goat, gold does not begin with a normal rounded o, but with a more centralized (neutral) vowel. This appears to be unstable, and realizations vary a fair bit: among younger RP speakers it may be more front, almost öu.
In the Anglo-Saxon period the centre of culture moved around England at different times, the last Saxon capital being Winchester in Wessex; but from the Norman Conquest it is the economic and political centre of London that has dominated English. The regional dialect around London was boosted by the writings of Chaucer and the foundation of the two mediaeval universities.
At some point - it is not clear when - there emerged a courtly accent that was not the same as the local accent. 'Speaking well' became distinct from 'speaking as they do in London'. Courtiers and educated people coming to London apparently adopted a London or court accent: evidence for this comes from those famous people who are specifically mentioned as not doing so (Sir Francis Drake, Sir Robert Walpole and Samuel Johnson retained their native Devon, Norfolk, and Stafford accents). By the 1700s there is clearly a low-class London accent which is not the educated or courtly accent. (Boswell records a Londoner saying vish for 'wish' in 1769.)
A recording of Florence Nightingale exists, who was born in 1820, and her accent sounds to me like a fairly standard RP. From the mid nineteenth century public schools such as Eton, Harrow, Winchester, and Rugby began deliberately instilling the prevailing prestige accent. Evidence is lacking of whether they had done so before. It was not actually taught, but those who spoke 'well' lorded it over those who did not, and conformism strengthened its position. (The schools did not all have exactly the same accent: it is sometimes possible to say that a man has e.g. a 'Harrow accent'.)
It is not confined to Britain either: e.g. in Australia many educated people, including ABC announcers, traditionally use an accent quite close to neo-RP, with only a few minor features marking them out as Australian.
Numerous alternative names for RP have been used: BBC English, the Queen's English, Oxford English, Public School English, Public School Pronunciation, Received Standard English, General British, etc. The Queen's accent is quite unusual, and is not a good example; BBC announcers traditionally used high RP but now mainly use a current form or received regional capital (e.g. Edinburgh, Belfast) accents.