His name is the Welsh word for good sense, prudence, deliberation — the faculty of thinking before acting. The First Branch of the Mabinogi is largely a demonstration of him not having it, and the tale is much better once you notice that the joke is in the title.
The discourtesy at Glyn Cuch
He is out hunting, gets separated from his companions, and hears another pack. In a clearing he finds a stag brought down by hounds he does not recognise: dazzling white, with red ears. He drives them off the kill and sets his own dogs on it.
A grey-clad rider arrives and says he will not greet him, because Pwyll has just done the greatest discourtesy he has ever seen — taking another man's kill. Not theft, note: discourtesy. In this literature that is the more serious charge.
The rider is Arawn, a king of Annwn, and the compensation he asks for is elaborate. They will exchange shapes and places for a year. Pwyll will rule Annwn wearing Arawn's face, and at the end of the year he will meet Arawn's rival Hafgan at a ford and strike him one blow — one only, because a second blow will heal him and he will fight again the next day.
A year of not touching someone else's wife
Pwyll goes, and takes over Arawn's kingdom, his court and his bed. Every night for a year he turns his back on the most beautiful woman he has ever seen and says nothing to her, and every day he is as affectionate as a husband. He never explains himself, because explaining would break the arrangement.
At the ford he kills Hafgan with a single stroke and refuses, with some difficulty, to strike again when the dying man begs for it.
When the two kings resume their own shapes, Arawn goes home and discovers what happened — or rather what did not — and the friendship that follows is permanent, with gifts of hounds, horses and hawks travelling between Dyfed and Annwn ever after. Pwyll is given the title Pen Annwfn, head of Annwn.
The heroism in the episode is entirely negative: not striking a second blow, not taking what is available, not talking. It is a story in which a man earns a kingdom by declining to do three things.
And then he loses it all by talking
The rest of the branch is the reverse. He goes to the mound at Arberth, sees a woman on a pale horse and spends three days trying to catch her instead of asking her to stop — the episode belongs properly to Rhiannon, who has the better of it throughout. Then, at his own betrothal feast, a stranger asks him for a favour and Pwyll grants it before hearing what it is. The stranger asks for the bride.
That is pwyll failing in the most complete way imaginable, and it takes his wife's ingenuity and a year's delay to undo. Rhiannon's verdict on him at the time is not gentle: never has a man been more feeble-witted.
He recovers his standing at the end, presiding over the return of the lost son and the shaming of the women who accused her. But the branch has established its pattern by then, and the pattern is that Pwyll is at his best when he restrains himself and disastrous when he speaks.
Dyfed, Arberth, and what is real
The geography is not invented. Dyfed was a genuine early medieval kingdom in south-west Wales, with a documented dynasty and, unusually, an Irish-derived royal line — the ogham-inscribed stones of Pembrokeshire are part of the same picture. Arberth is Narberth, a real town. The Four Branches are set in a Wales that a twelfth-century audience could locate on the ground, and the supernatural enters that landscape rather than replacing it.
He is also, in the Welsh Triads and in later poetic reference, a figure with a reputation independent of the Branch — which suggests the surviving tale is one treatment of material that was more widely known.
Is Annwn the Welsh land of the dead?
Not in this text, and the assumption causes a lot of confusion. Arawn's Annwn has courts, feasts, hunting, a rival king, a territorial war and a queen; nobody in it is dead, and Pwyll rules it for a year without remarking on anything funereal. It is another kingdom that happens to be difficult to reach. Later Welsh material — and a great deal of modern writing — pushes it towards a Celtic hell, partly under Christian pressure and partly because the poem Preiddeu Annwfn describes a raid on a fortress from which almost nobody returns.
What is the point of the one-blow rule?
It is a rule about finality, and it recurs in Celtic-language narrative: a second stroke undoes the first. Hafgan can only be killed by a man who is willing to stop, and Arawn — who has fought him annually for years — apparently cannot. The condition tests exactly the quality Pwyll's name denotes, which is why the substitution is required at all: Arawn does not need a better fighter, he needs someone capable of not finishing a job.
Does Pwyll appear in the other branches?
Only as a memory. He dies between the First and Third Branches, and his significance afterwards is carried by his son Pryderi and by his widow's second marriage. But the Head of Annwn title, and the alliance he made by keeping his hands to himself for a year, remain part of Dyfed's standing in the later tales — one of the few things in the Mabinogi that stays fixed while everything around it goes wrong.