"The Destruction of Sennacherib" makes extensive use of simile. As a whole, this gestures towards how classical epics like The Iliad use simile, thus linking the poem to a larger culture of war poetry and also appealing to readers who would have been familiar with classical literature.
Byron's poem focuses in particular on comparisons with the natural world. One reason for doing so is that this links human events with nature, thus suggesting that there's not that much difference between what happens to people and what happens to things in the natural world. For instance, the poem's final simile, in its closing two lines, states that "the might of the Gentile ... / Hath melted like snow in the glance of the Lord!" Here, human decline gets compared to a late winter thaw, as if both are aspects of the same unavoidable process.
As in the above example, the poem's comparisons with the natural world also establish an equivalence between God and nature. Here, the poem implicitly compares the "glance" of God to the sun's warmth as it melts snow. In this way, although the events of the poem are extraordinary (God sends the Angel of Death to wipe out a whole army overnight), these natural similes serve to fit them into the ordinary course of the natural world. So, while the way the Assyrian soldiers died is remarkable, the simile emphasizes that the fact they died is unremarkable; after all, everyone will die sooner or later.
Relatedly, the first stanza's similes employ natural imagery that comes from the Bible. "[T]he fold" in line 1 follows the Christian tradition of referring to believers as sheep. And "Galilee" in line 4 refers to the Sea of Galilee, which figures prominently in the Bible (especially the New Testament). Both of these instances further link religion, nature, and human beings.
The similes in stanza two, which compare the destruction of the Assyrians to the transition in foliage between summer and fall, provide the poem's clearest statement of the parallel between human decline and natural rhythms. This theme is also expressed in the fourth stanza when the poem compares the foam at a dead horse's mouth to the spray of surf. Additionally, the sea imagery here picks up on the earlier reference to the Sea of Galilee, showing how all of these various natural processes are linked in an unbroken cycle.
All in all, these comparisons depict the interconnection between entities as varied as humans, animals, leaves, seas, snow, seasons, angels, and God. The human, the natural, and the divine all bleed into each other.