Carpe diem is Latin for "seize the day." This was a popular theme in seventeenth-century poetry, as this was a time of uncertainty and upheaval in England. "Seize the day" means grab your pleasures now, because you don't know how long you have left before you die or life changes.

In this poem, Marvell's male speaker is trying to persuade his female beloved to have sex with him. He does this, first, by using hyperbole or exaggeration. For instance, he says he would gladly spend a hundred years complimenting her eyes, or two hundred years praising each of her breasts, but there simply isn't time: our days on this planet are finite and fleeting.

Marvell then uses fear to try to persuade his mistress to seize the day. He reminds her that her beauty will be useless in death and that nobody "embrace[s]" or sings in the grave. Finally, he conjures a compelling image of urgency in what some critics have called the most famous couplet of the seventeenth century, saying,

But at my back I always hear

Time’s wingèd chariot hurrying near.

He employs the image of a horse-drawn chariot galloping at them as a metaphor for time's speed; we today might use the image of a speeding rocket ship or airplane.

Marvell's speaker also uses violent imagery to imagine their lovemaking as fighting back against time, such as when he suggests to his lover that they

tear our pleasures with rough strife

Through the iron gates of life.

Life is short at the best of times, but it was especially short in Andrew Marvell's day. When he wrote “To His Coy Mistress,” life expectancy was much lower than it is today, and this gives added urgency to his theme of carpe diem or “seize the day.”

Simply and crudely put, the speaker of the poem wants his beloved to go to bed with him. Being a poet, however, he uses flowery language to get her into his bed. And being a metaphysical poet, he uses the carpe diem conceit as a way of driving his point home.

The speaker attempts to seduce his lady by getting her to focus on the limited time available to them both in this world. If they had “but world enough and time,” in other words, if they had all the time in the world, then of course this wouldn't be a problem. But given that their time is limited, that “time's wingèd chariot” is “hurrying near,” it's all the more reason for them to make the most of what little time they have left and indulge their carnal desires to the full.

It's fair to say, however, that the speaker's emphasis on death—most notably his reference to worms taking his beloved's “long-preserved virginity”—does tend to overshadow the erotic passion he clearly wishes to express.

"Carpe diem," as you probably already well know, means "seize the day" or, less literally, "make the most out of the time we have." The phrase is often credited to the Roman poet Horace (or Quintus Horatius Flaccus). It's a pretty common sentiment in literature. For example, Henry David Thoreau talks in Walden about "want[ing] to live deep and suck all the marrow out of life."

Andrew Marvell's poem "To His Coy Mistress" opens famously with the assertion that, if we had all the time in the world, we would have no need to hurry with our passion:

Had we but world enough, and time,
This coyness, lady, were no crime.

The second section counters this first section by making clear that we, in fact, do not have al the time in the world:

But at my back I always hear
Time's winged chariot hurrying near;

The third and final section of the poem brings this argument to a close ("therefore") by urging the "coy mistress" to act with him now on their love:

Now therefore, while the youthful hue
Sits on thy skin like morning dew,

Most readers see this poem as presenting a thinly-veiled and self-serving argument. The speaker wants a woman to go along with what he wants, which is her now. The sentiment of "carpe diem," apparently, can be either thoughtful or superficial.

The term "carpe diem" means "seize the day."  In modern English we would probably say it as "take what you can get, when you can get it."   In other words, don't put things off -- life is short.

Given this, you should be able to see how this theme is shown in the poem.  The speaker is telling his love that if life wasn't short, he would be really patient.  For example:

And you should, if you please, refuse
Till the conversion of the Jews.

But, in the second stanza, he says that time is flying by.  Because of that, there's no point in waiting.  He says that they should start sleeping together sooner rather than later.  Otherwise,

And your quaint honour turn to dust,
And into ashes all my lust.
The grave's a fine and private place,
But none I think do there embrace.

This is very much a "carpe diem" idea -- we will soon be dead, let's live life now and not wait for later.