AKA ogyrwen or gogyrwen
A difficult subject, somehow related to the medieval Welsh concept of awen.
Some say ogyrven is a cauldron, while Pughe's dictionary says it is a "a spiritual being or form; a personified idea." Skene equates the term with Cerridwen, while Iolo Morgannwg claimed it was what the three rays of awen /|\ represented. The word itself may mean "youthful fair one" (og- youthful; wen > gwen "fair/white/blessed (female) one"). But as for what exactly ogyrven is--and is not--is up for debate.
The relevant texts can be found in the Book of Taliesin and the Black Book of Carmarthen; most of the references are attributed to Taliesin, while at least two can be traced to Cuhelyn, a little-known bard, presumably of the sixth or seventh century:
Fynedic. waud. fruythlawn. traethaud trybestraud heid.
Hervit urten autyl kyrridven ogyrven amhad.
Amhadanav areith awyrllav. y cavkeineid.
A successful song of fruitful praise, relating to the bustling course of the host,
According to the sacred ode of Cyridwen, the goddess of various seeds,
The various seeds of poetic harmony, the exalted speech of the graduated minstrel
--att. Meigan, BBC III
Here, ogyrven is translated as "goddess", refering to Cerridwen, who is the goddess of seeds of poetic harmony. Elsewhere, however, it's left untranslated; again, Cuhelyn:
According to the sacred ode of Cyridwen, the Ogyrven of various seeds,—
The various seeds of poetic harmony, the exalted speech of the graduated minstrel,
Cuhelyn the wise, of elegant Cymraec, an exalted possession,
Will skilfully sing;
The meaning of ogyrwen here is still unclear.
"Taliesin" also mentions it:
Shall not my chair be defended from the cauldron of Cerridwen?
May my tongue be free in the sanctuary of the praise of Gogyrwen.
The praise of Gogyrwen is an oblation, which has satisfied
Them, with milk, and dew, and acorns.
--"Kerd Veib am Llyr" LT XIV
High when came from the cauldron
The three awens of Gogyrwen.
--"Kadeir Teyrnon" LT XV
Inspiration without mediocrity,
Seven score Ogyrven
Are in the Awen
--"Angar Kyfyndawt" LT VII
And so awen is of ogyrven, and ogyrven is in awen, but they are not thing. Then what is ogyrwen? If an ogyrven is a goddess like Cerridwen, are there three divine inspirations coming from the Goddess? Are there seven-score goddesses inside the divine inspiration?
However, is "goddess" the right word? The phrase repeated in BBC III and IV--"Ogyrven amhad"--can be translated not only as "ogyrven of various seeds" but "Ogyrven’s offspring"--Cerridwen, the savage Muse, is then not the goddess of various seeds, but the offspring of "Ogyrven". Again, what is ogyrven?
I have seen some references to the word Ogryfan being a name for Gwenhyfar's father; this is based on the Welsh Triads:
Three Great Queens of Arthur: Gwennhwyfar daughter of Cywryd Gwent, and Gwenhwyfar daughter of Gwythyr son of Greidiawl, and Gwenhwyfar daughter of Gogfran the Giant.
Unsurprisingly, it's Robert Graves who makes the most of this in his The White Goddess, wherein he draws a connection between his concept of Bran (who he sees, with Bran's uncle/brother Beli as a type of Apollo, god of poetry and of the Muses) and "Ogyr Vran." He didn't entirely invent this association; it goes back to John Rhys' Lectures on Welsh Philology, where he mentions Ogyrfran as ‘Ocurvran’, "evil crow," and repeating what he says was a well-known rhyme:
Gwinevere, giant Ogyrvan’s daughter,
naughty young, more naughty after
But while her father is certainly named Gogfran, there is no good reason to tie this to ogyrven. The name, it seems, is possibly an interpolation from Irish genealogies, later appended in the Romantics' minds, who mention Gogfran as the Welsh god of poetry--something for which there is no medieval basis, which explicitly makes Cerridwen the origin of awen.
The relevant Irish genealogies from Rawlinson B 502--The Book of Glendalough--go like this:
¶36] Item. Find Fili de filiis Ailb m. Augein Aurgnaid cecinit:
1. Báeth buide bánán dron
dána dílmain maicne n-Ailb áirme.
2. Achir búire brú di derg
Dondobur dóel Gabruan ginne fur Findubur.
Do-roíbatar in sin h-uili.
Also, Find the Poet sang of the sons of Alb son of Augen the Servant:
Baeth the yellow, firm little white one
Of unimpeded talent, the numerous progeny of Alb.
Achir the furious, belly of red (or "red spear"?),
Dondubur the beetle, Gabruan who was begotten upon Findubur.
That was all of them.
The name Findubur--or Findabhair--means "white (fair) phantom", which is the same meaning of "Gwenhyfar." It has been suggested then that Gwenhywfar daughter of Gogfran is derived from Findubur mother of Gabruan; it wouldn't be the first time Irish names and genealogies ended up in a mutated form in Welsh literature.
Sadly, I have no conclusions to make--unfortunately, Old and Middle Welsh is sufficiently obscure enough that multiple translations of a poem of Taliesin's could produce works that barely resemble each other. Moreover, the influence of romantics and forgers like Iolo Morgannwg has dirtied the water substantially, making it difficult to decide what is legitimate, and what is suspect.
What is ogyrven? No one seems to agree on the definition, and many definitions--that it's a cauldron, that it's Gwenhyfar's father, that it's a goddess--seem to be built upon mistakes or rank speculation.
Our knowledge of the medieval bardic schools is shoddy; moreso the true history of the poems of "Taliesin" and his contemporaries. What they called ogyrven may never be fully understood.
"The Rawlinson B 502 Genealogies." Corpus genealogiarum Hiberniae. Michael O'Brien (ed), First edition (1962); reprinted exactly, Dublin 1986 (apart from a short introduction (pages ix--xvi) by John V. Kelleher, largely devoted to explaining O'Brien's hitherto unexplained sigla and abbreviations). School of Celtic Studies, Dublin Institute for Advanced StudiesDublin (1962) Corpus of ELectronic Texts (CELT) website. URL: http://www.ucc.ie/celt/published/G105003.html
Graves, Robert. The White Goddess. p.75-76.
Hunt, August. "An Identification of the Three Guineveres" Vortigern Studies, 2002. URL: http://www.geocities.com/vortigernstudies/articles/guestdan16.htm
Trioedd Ynys Prydein. ed. and trans. Rachel Bromwich. Cardiff: UWP, 1963.