The word Monster is derived from Latin, and shares a root with the word "demonstrate". Monere means "to warn or instruct", and the peculiar uniqueness of the monster is that by its very aberrance, we are able to infer what is "normal" or "proper".
Monsters are provably fictitious. Even the monsters with their roots in real life - be they giant squid, white whale, great white shark, Tyrannosaurus Rex, or tropical spider - are only "monstrous" because of our reaction to them. Monstrosity is a human construct. It is an overlay, superimposed artificially onto its subject to reflect our own fears and vulnerabilities.
Monsters do not choose to be monstrous. Whether born, made or imagined, they are hideous from conception, and live out their fate without choice. They are incapable of making moral decisions - a good monster's description includes not only its appearance but its behaviour. Monsters who escape their own monstrosity by making decisions (think Shrek, The Beast and the Iron Man) are no longer monstrous - they are characters. The true monster can therefore be properly understood as a narrative device, bound to its author's script, and without agency or personality of its own.
If monsters can't make choices or influence their own fate, then what on Earth are they doing in a narrative? In fact, it is their very lack of agency that imbues them with their greatest value.
They can be made as strong, as fast or as hideous as the author's imagination allows. What better way to force a hero to face the inevitable? They are shielded from reason, and cannot be negotiated with. What better way to push a clever coward into a transformative conflict? But most of all, in their hideousness, monsters are living violations of our moral and aesthetic sensibilities. They are built out of broken rules and jarring statements of offence. How else can we reassert our own justifications for our loathing of ugliness, violence or sacrilege? Monsters provide more than obstacles for a story's characters. They allow us to calibrate our moral compass within the context of the story, and so bind our empathy to the events of its narrative. More powerfully still, they have an outward effect; through them, we can use stories to justify our real-life morality.
After all, were we to lose sight of our taboos, monstrous things would seem normal to us - and the thought of that is hard to bear. In this context, the power of disgust is what links our emotive responses to our sense of cold reason. Monsters allow us to rationalise and explain these feelings. They are a conjecture, like the virtual image we "see" in a mirror: inferred from the suppositions that surround it, crystal-clear, perfectly informative, but not even slightly real.
So how do Homer's monsters warn or instruct us? Several examples spring to mind. It is the presence of the monstrous Cyclops that first tells us that we have moved from an heroic narrative to a mythical one, where unfathomable forces loom larger and closer than ever before. The Sirens make a strong analogy for the power of reason over temptation, and shortly afterwards, Scylla and Charybdis can be cogently read as symbolic of a leader's burden to choose in the face of unavoidable loss.
And the Laestrygonians? Being the first manifestation of Poseidon's curse, do they represent man's powerlessness against the divine? As a direct consequence of the mutiny, might their depravity illustrate the ruin that follows from the breakdown of social hierarchies? Or is there something more going on? Perhaps all three. Three thousand years later, we're still trying to work it out.