As I noted in my comment, that quote refers to a welsh triad, sometimes translated as "Three Prostrate (Humble) Chieftains of the Island of Britain":
Llywarch the Old son of Elidir Llydanwyn,
and Manawydan son of Llyr Half-Speech,
and Gwgon Gwron son of Peredur son of Eliffer of the Great Retinue.
(And this is why those were called the 'Prostate Chieftains': because they would not seek a dominion, and nobody could deny it to them.)
(Bromwich, Rachel, Trioedd Ynys Prydein: The Triads of the Island of Britain.)
I'm not sure what you mean by "connection." I don't think the three characters ever met, although I could be wrong. The Mabinogion is filled with references to various triads, so for the welsh audience it would have been interpreted as a reference to another piece of literature. The triads themselves are essentially catalogues of welsh stories (grouped in threes).
I suppose I could elaborate on what was meant by "Humble Chieftains": it basically meant that they had land taken from them (Bromwich).
If you're interested in learning more, the wikipedia pages for Llywarch, Peradur (father of Gwgon Gwron) and Manawydan would be good places to start. Llywarch in particular is mentioned in several welsh poems (other than the triads).