In the first two lines, we find the poem's first example of hyperbole, or overstatement. The speaker says,
Had we but world enough and time,
This coyness, lady, were no crime.
The speaker implies that the lady to whom he speaks is committing a crime by being coy with him. In other words, she is being playfully flirtatious but, ultimately, refuses to sleep with him. By implying that her behavior is criminal, the speaker is setting a rather playful, even humorous mood. Obviously coyness isn't illegal, and so this is a clear example of hyperbole to suggest that it is. We might also chuckle at the speaker's clear sexual frustration.
Further, the speaker says that, if they had all the time in the world, then
[His] vegetable love should grow
Vaster than empires and more slow;
An hundred years should go to praise
Thine eyes, and on thy forehead gaze;
Two hundred to adore each breast,
But thirty thousand to the rest;
An age at least to every part,
And the last age should show your heart.
These lines present further examples of hyperbole. The speaker says that, if time were not a consideration for him and his lover, he would allow his love to grow slowly, and it would grow bigger than empires. He would dedicate a century to praise her eyes and forehead, four centuries total for her breasts, and so on. These examples of hyperbole, concerning empires and suggesting that he would spend literal centuries to admire various parts of her person, end finally with the claim that he would spend an "age" to admire her heart. Their effect, then, is to impact the reader with the speaker's affection. There may be some playfulness and humor, but it does seem as though the speaker earnestly cares for his lover.