What quote reflects the nature of Odysseus' quest in the Odyssey by Homer?
This is a great question. The chief theme of the book is the idea of homecoming. Odysseus desires to go home to reunite with this family, son and city. However, there are obstacles along the way, which make it extremely difficult. In light of this the opening words of the Odyssey is an apt description.
"Sing to me of the man, Muse, the man of twists and turns driven time and again off course, once he had plundered the hallowed heights of Troy. Many cities of men he saw and learned their minds, many pains he suffered, heartsick on the open sea, fighting to save his life and bring his comrades home."
Another time where this idea comes to the fore is when Calypso, who has him as his love hostage tries to persuade him to stay with him. She acknowledges that Odysseus wants to go back home. She also gives him a realistic prophesy of the difficulties that he will have on his journey. She says:
"So then, royal son of Laertes, Odysseus, man of exploits,
still eager to leave at once and hurry back to your own home, your beloved native land? Good luck to you, even so. Farewell! But if you only knew, down deep, what pains are fated to fill your cup before you reach that shore, you’d stay right here, preside in our house with me and be immortal."
As we read the work, book after book, there are hardships and exotic encounters. And even when he arrives at home, there are more troubles. Hence, we can say the nature of Odysseus' journey is that it is fraught with difficulties, but in the end he makes it home.