This is an interesting question. As others have already pointed out, Heracles doesn't actually have much of a presence in the Odyssey itself. This should not be surprising, considering that Heracles belongs to an earlier generation of heroes. But perhaps one could argue that, even so, he's actually a lot...
This is an interesting question. As others have already pointed out, Heracles doesn't actually have much of a presence in the Odyssey itself. This should not be surprising, considering that Heracles belongs to an earlier generation of heroes. But perhaps one could argue that, even so, he's actually a lot more important to the Odyssey than one might assume, if we look at the Odyssey within the larger context of Greek heroic literature rather than viewed in isolation.
Consider the thematic underpinnings which tend to be central to the stories of Heracles. If we look at the world in which Heracles emerges, we see one that's actually deeply threatening to human flourishing. Just consider the Twelve Labors and the nature of his exploits. One of the critical themes that emerges within Greek heroic literature is the safeguarding of civilization, and a major part of why Heracles emerges as the greatest of all the Greek heroes is because he, more than any other, tames the dangerous forces which would threaten it (i.e., civilization). To what degree might we say that the exploits of Heracles's generation ultimately have shaped the world as Odysseus and his generation know it? It's an interesting question and one worth asking as far as this question is concerned.
With that in mind, now consider the story of Odysseus himself: thrown off course to travel across dangerous seas, Odysseus is thrown from the relative security of civilization into the dangers which lie beyond it. In a certain respect, one might even say that Odysseus's own encounters represent an echo of those earlier heroes. They conquered those dangerous forces and pushed them towards the edges of human habitation, but now we have Odysseus, who must confront the forces which still linger outside these bounds.
It's a difficult question because, viewed in isolation and separate from the larger traditions of Greek heroic traditions, it appears as if Heracles has very little importance to The Odyssey. Moreover, I don't think this claim is by any means incorrect (it seems a valid interpretation). Looking at it from a wider context, however, of how The Odyssey fits into that larger literature and how the Greeks themselves may have viewed the world around them, then I think things might start to look more murky.