Some say the world will end in fire
Some say in ice.
From what I’ve tasted of desire
I hold with those who favour fire.
Since the Common Era (CE/BCE), people have predicted catastrophic events that would result in the extermination of humanity, the collapse of civilisation, or the destruction of the planet. The poem, however, deals with the question of "what" would likely cause the apocalypse.
The speaker begins the poem by explaining two major viewpoints existing in society. He says, "Some say the world will end in fire / Some say in ice". There seems to be a debate about how the world is going to end, and one section of the society believes that fire would cause the ultimate destruction, while another set of people argue that it is going to be the ice.
Initially, we are made to think that the speaker is talking about the elements called fire and ice. Too much heat can destroy lives on a planet. For instance, studies prove that life on Mercury is not possible because of its proximity to the Sun. Extreme heat on the planet has made the surface impossible for vegetation or life form to appear and survive.
Fires have also caused several devastations on Earth. For instance, "fire can destroy your house and all of your possession­s in less than an hour, and it can reduce an entire forest to a pile of ash and charred wood. It's also a terrifying weapon, with nearly unlimited destructive power. Fire kills more people every year than any other force of nature."¹ Being the most destructive of all powers, the amount of devastation and panic it can cause is incredible. 
Fires had a strong presence in most of the terrible wars that we have fought. During the classical and mediaeval periods (approximately between the \(8\)th century BC and the mid-\(16\)th century AD), heat or burning action was used in battles. With the advancement of technology, gunpowder was invented, which improved the effectiveness of weapons starting with fire lances and eventually leading to the invention of cannon and other firearms. Modern military weapons like napalm, flame throwers, and other explosives have direct ancestors in the early thermal weapons. Modern strategic bombing still employs fire-raising and other destructive tactics.
When talking about the apocalypse (the final destruction of the world), it is interesting to observe that some religions and mythology have predicted fire (but in different forms) to be the cause of the world's end. According to an article on CNN, "Zoroastrians believe that the earth will be devoured by fire".²

Hence fire, in its physical form, acts as a catalyst for destruction. The speaker also agrees with the argument that the world would end in fire. He says, "From what I’ve tasted of desire / I hold with those who favour fire." However, he uses fire as a metaphor here. He claims that extreme passion (or desire) will be the cause of destruction. To quote the Free Press Journal, "the passions of human beings such as lust, hatred, greed and worry are vicious fires that can destroy the soul and damn it to suffer in the fires of hell".³
So, how are fire and desire connected? To begin with, both share similar physical traits: fire produces heat, whereas ignited passion/desire also leads to an increase in bodily temperature. When you begin to observe, one would realise that neither of them is always destructive. Fire, when controlled, becomes a necessity. It provides warmth and light, cooks food (making it more edible), and is used for technological development. As Professor Jonathan Charteris- Black writes, "controlled fire is therefore a source of physical comfort and cognitive development".⁴  It only becomes a destructive force only when it is manipulated and uncontrolled.
Similarly, uncontrolled and unjustifiable desires can result in catastrophic events. For instance, imperialism is one of the primary reasons why battles are fought. It is worth noting that the poem was published only a couple of years after the end of World War 1. The speaker writes, "from what I’ve tasted of desire", suggesting the after-effects of the war was still fresh inside him—the desire for power and to conquer led to a war of such magnitude. So, the speaker feels certain that the desire, as strong, wild, manipulative, and uncontrollable as fire, can cause the world to end.
Meanings of difficult words:
TasteTo have experience of
DesireTo want something, especially strongly
HoldTo have a belief or opinion; to support
FavourTo feel or show approval or preference for
ApocalypseAn event involving destruction or damage on a catastrophic scale;
the complete final destruction of the world, as described in the biblical book of Revelation
AztecsA member of the indigenous people dominant in Mexico before the Spanish conquest of the 16th century
ZoroastrianismAn Iranian / Persian religion and one of the world's oldest continuously-practiced organized faiths, based on the teachings of the Iranian-speaking prophet Zoroaster
ImperialismA policy of extending a country's power and influence through colonization, use of military force, or other means
National Council of Educational Research and Training (2007). First Flight. Fire and Ice-Robert Frost (pp. 15). Published at the Publication Division by the
Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.