This poem is structured like a rhetorical argument. The poem can be divided into three sections : if (I had all the time in the world); but (we don't); therefore(we should act). The poem is an elaborate and eloquent argument to having sex.
In the first section of the poem, the "if" section, the speaker tells his coy mistress that if they had all the time in the world they would first explore the world separately, and that once they met he would spend many, many years to adore each of her body parts. Nothing would be rushed; there would be no need for haste.
In the "but" section of the poem, the speaker brings their situation back to reality. In reality he hears "time's winged chariot hurrying near." Time is always moving forward and we are all on our way to the vast eternity of death. In this section he rather explicitly tells the young lady that once she dies and is in the "marble vault . . . then worms shall try that long preserved virginity." He is suggesting that she might as well lose her virginity to him in her lifetime when she can enjoy it, otherwise the worms will get it eventually. He is trying to creep her out! He ends this part of the argument by reminding her that the "grave's a fine and private place, but none, I think, do there embrace." The grave may be private, but is not a fun, warm, or loving place.
The final aspect of the argument is that they should embrace carpe diem -- seize the day-- and enjoy their sexuality. He uses several images that suggest youth and passion. He comments on the "morning dew" which uses the day of life metaphor to reference her youth. He mentions "instant fires" which is a stock metaphor for passion. He draws the image of "amorous birds of prey" which suggests physical energy and passion. He uses the image of them rolling their "sweetness up into one ball" which suggest sexual joining, while "tear our pleasures with rough strife thorough the iron gates of life" is likely a reference to the hymen being broken upon intercourse. The language is vivid and strongly sexual because he is making the final point of his argument. First he flatters her, then he points out reality, and he ends it with language that entices her to believe his argument.