The Odyssey is a Greek epic poem formed by 24 parts attributed to Homer, it is considered to be the sequel of the Iliad. It is supposed to have been written in VIII B.C
It narrates the return of the Greek hero Odyssey or Ulises in Roman culture, to his home from the Trojan Wars. The story tells the adventures of Odyssey spending ten years on the war plus ten more years in his return home, at the Ithaca Island. His son Telemachus and his wife Penelope have to withstand a group of men trying to marry Penelope but at the same time consuming the house’s riches. Odyssey finally gets back at his home disguised as an old man so nobody would be suspicious of him and would try to stop him. He kills all the men trying to marry his rightful wife. The best weapon that Odyssey has is his intelligence, courage and the help of the Goddess Athene.
Argus was the hound of noble Odysseus, in this section Eumaus is talking to Odysseus when he is disguised as an old man to face the "suitors" in his own home, Eumaeus does not know that he is telling the story of Argus to its own owner.
So, to give a final and concrete answer to this question, Eumaeus is talking about:
Odyssey, who is disguised as an old man.