Cú Chulainn is a famous character from Irish myth, and the accidental slaying of his son is part of the legend. On Baile's Strand is a retelling of parts of the myth, with some added subplots and comedy. Yeats, being Irish, would have presumed his audience was familiar with the rest of the story already.
In the myth, the young Cú Chulainn travels to Scotland to train with the famed warrior-woman Scáthach. While there he fights against Scáthach's fierce rival Aífe and becomes the first person to beat her. He agrees to spare her life in exchange for her bearing him a son.
When the son is 8, and already a fierce warrior, he travels to Ireland to find his father. In some versions of the tale he is sent by his mother to kill Cú Chulainn in revenge for his marrying another woman, and she tells him never to identify himself to his foes. For whatever reason, the boy fails to claim his identify and is slain by Cú Chulainn, who has never seen his son, as an invader. When Cú Chulainn finds out, he is grief stricken.
There's a good Wikipedia page on Cú Chulainn. Here's what it says specifically about the death of his son:
Eight years later, Connla, Cú Chulainn's son by Aífe, comes to Ireland in search of his father, but Cú Chulainn takes him as an intruder and kills him when he refuses to identify himself. Connla's last words to his father as he dies are that they would have "carried the flag of Ulster to the gates of Rome and beyond", leaving Cú Chulainn grief-stricken.
The fullest version of this story is known as Aided Óenfhir Aífe (The Death of Aífe's Only Son) and is found in a manuscript known as The Yellow Book of Lecan. Apparently Yeats used this text as the basis for On Baile's Strand as well as a poem, Cúchulain's Fight with the Sea.
I have been unable to source a definite translation, but here is the relevant text from what appears to be one:
What was the cause of the death of Cú Chulainn's son? Not difficult.
Cú Chulainn went for weapons instruction to Scáthaig the Foam-white daughter of Airdgeme in Letha to gain mastery of feats with her and he went to Aífe daughter of Airdgeme and he left her pregnant and said she would bear a son.
‘Take this thumb-ring of gold to hold', he said, ‘until it is fit for the boy. When it is fit, let him come to seek me in Ireland and not give way to a single man on the road and not declare himself to a single man and not refuse combat to a single man.’
The son went one day seven years afterwards to seek his father.
Then he went after the boy in the water, until with deception the gaí bulga was used, because no person had been taught that weapon by Scáthach but Cu Chulainn alone. He shot it at the boy through the water, so that his entrails were at his feet.
‘It is that indeed,’ he said, ‘this Scáthach did not teach me! Woe that you have wounded me!’ said the boy.
‘It is true,’ said Cú Chulainn. He took the boy then in his two arms, and carried him over there and carried him before the men of Ulster.
‘Here is my son to you, oh Ulstermen,’ he said.
Here's another possible translation, a little more embellished for the modern reader, courtesy of user @rand-althor.
If my memory serves me correctly, there's a longer and more detailed version of the story, compiled from a variety of sources, in Thomas Kinsella's translation of the Táin Bó Cúailnge, in which he included a number of stories relevant to, but not directly part of The Tain.
- ^ James MacKillop, Dictionary of Celtic Mythology, Oxford University Press, 1998, pp. 5-6