In Lord of the Flies, for what do the boys offer the sow's head to the beast?
Here's the bit of the novel you need, from Chapter 8, titled "Gift for the Darkness":
Jack spoke loudly.
“This head is for the beast. It’s a gift.”
The silence accepted the gift and awed them. The head remained there, dim-eyed, grinning faintly, blood blackening between the teeth. All at once they were running away, as fast as they could, through the forest toward the open beach.
The sow's head is given as a gift to the beast out of sheer, straightforward fear. It's an admission of superiority, as Jack sees it, an acknowledgement that Jack too is scared of the beast, and that the beast might be pacified with gifts like some sort of dark god.
What do the boys think the beast will do with the sow's head? Who knows? The book doesn't actually tell us directly. But the point is clear from the way Jack does it, and from the way the boys run away as soon as the gift of the sow's head becomes associated with the beast. The sow's head is a sort of bribe, a desperate hope that it might stop the beast from attacking them.
Irony is, of course, there is no actual beast. It's an offering given in fear, to fear.