"Desire" is meant to be closely associated with love. Of course, love has many other sides: commitment, affection, and responsibility, to name a few. But desire is one of the most fundamental emotional response to being in love, and it's also the most potentially destructive. You can think of desire as a huge store of energy that can be channeled or directed in many different ways. "Fire and Ice" argues that, if channeled in the wrong way, desire could bring about the end of the world. There are other kinds of desire than erotic love – you can desire a cool sports car, for example – but romantic desire is probably the most powerful.
The speaker's mention to "desire" refers especially to sexual desire.
"Desire" is not necessarily a destructive force in the poem, and its ability to "end the world" could actually be a good thing.