To his coy mistress... This poem was written in seventeenth century and includes some words, which changed their usage and meaning during 300 years. So first of all I would like to explain what words 'coy' and 'mistress' meant in the period of Metaphysical poetry. When somebody was coy, especially the woman, it meant that she was very shy, reserved and she did not behave in a flirting way. It related in particular in a realm of love or sex. The word 'mistress' is very closely connected with this because a mistress was a woman who had a sexual relationship with usually married man but he was not her husband.
After first reading of this poem you may think that the argument is simple - a man encourages his mistress to be not too shy and be more glowing. It is something like love or ticklish utterance to her, a small appeal for her.
But this would be very unsophisticated for Andrew Marvell, a Metaphysical poet. Through the whole poem passes a motive 'carpe diem'. It is a Latin locustion from the verses of Quintus Horatius Flaccus, a Roman poet and satirists who lived in antiquity. Carpe diem means 'seize the day'.
We could divide this song into 3 parts. The first one begins with the first line and finishes by the twentieth. In this part speaker blandishes to his woman, he entices her and he says her how much he loves her. Already in this part Marvell refers to the problem of time. In the first two lines "Had we but world enough, and time, this coyness lady, were no crime" he intimates her that if the time would be never-ending and so they have a plenty of time, her demureness would be on the place. But everybody...