John Donne opens this poem with another conceit, and while it is not the central comparison of the poem, it does establish the point of the poem and the gives a context. Donne is telling his love that he must be away, and they will have to part soon. He tells her that he wants their parting to be as subtle as that moment between life and death. This seems like a strange comparison, hence it is considered a conceit. He elaborates how they should behave in the first two lines of the second stanza, stating he wants no outward show of their emotion upon parting. This leads to his ultimate point -- that the two of them have a love that is greater than most, and therefore, doesn't need a public display; in fact it would be debase their love.
John Donne is the spearhead of the Metaphysical school of poets, famous for their conceitful style. Conceit is a typically Metaphysical trope, operative as a distant and far-fetched comparison between two radically unlike objects with a stress on wit and intellectual appeal. It is often defined as a violent yoking of heterogeneous elements or ideas. It is device of condensation in Metaphysical verse.
In Valediction: A Forbidding Mourning, the conceit involves a comparison between the twin spirits of the lovers and the two legs of the compass. One remains stagnant in its central position while the other rotates around it in a pursuit of love, as it were. This odd and rather peculiar comparison is operative at the level of sarcasm and undercuts the cliched romantic imagery regarding Platonic lovers.