"Twenty years gone, and I am back again."
Odysseus speaks these words quietly to his old nurse Euryclea, who washes the feet of what she thinks is a beggar who has come to stay for a while at the royal palace in Ithaca.
When Odysseus returns after twenty years of absence (Trojan War, 10 years, and another 10 years to reach his homeland after the end of the war), his son Telemachus is a grown man, his wife Penelope is beleaguered by suitors who each want her hand (and the money that comes with it) in marriage and have settled in the royal palace, eating and drinking away her fortune, until she will decide whom to marry; and his father Laertes lives in the hills with the shepherds. The goddess Athene, his mentor, has disguised him as a beggar, who came to the royal palace to ask the queen, Penelope, for alms.
Penelope does not recognize him, and this is what Odysseus intended. His disguise has a two-fold purpose, a) he can see first-hand if his wife is still faithful to him (although he has had his share of amorous adventures during his 10 years of journeying back to Ithaca), and b) he is safe from the suitors and has time to plan their demise. After all, strength lies in numbers, and the suitors number over 100. Without an advantage, such as a disguise, Odysseus cannot hope to succeed in avenging the honor of his family and his house.
So, Penelope kindly offers the poor beggar (aka Odysseus) a footbath to be performed by his old nurse, Euryclea, who recognizes her master by a scar on his leg. Odysseus received the scar when he was hunting boars on Mount Parnassus with his grandfather Autolycus. In order to prevent Euryclea from giving him away, he grabs her by the throat with his right hand and with his left draws her close to him, and warns her not to reveal his true identity. That is when he utters the words, "Twenty years gone, and I am back again, and asks her not to say anything about him returning to any one else in the house.
As the rightful owner of the title of king of Ithaca (and of Penelope), it is his right to restore his bruised honor by calling the suitors on their violation of his rights, killing them as a consequence.
According to patriarchal tradition, he is also entitled to test his wife's faithfulness. As it turns out, Penelope has nothing to fear (she is, after all, the epitome of faithfulness), but her treacherous maids, who have aided and abetted the suitors, will have to suffer the consequences.
When Odysseus returns to Ithaca, it's judgment day, He restores the honor of his house, rescues those who have been faithful and loyal to him (his wife, his nurse, his father, his son) and kills those who were illoyal (the maids) and tried to usurp his powers (the suitors).
Although it looks as if Odysseus was doing it all by himself (he singlehandedly kills all 112 suitors with his bow), it is only due to divine intervention (Athene who disguises him as an old man) that he prevails.