The speaker of "To His Coy Mistress" is a man, as evidenced by the masculine pronoun used in the title. He is smitten with a young lady, the "mistress" of the title, and tries to seduce her to move quickly in their courtship. This is an example of a carpe diem poem, in which a speaker encourages someone to seize the day: in this case, he is trying to persuade this young mistress to enjoy earthly pleasures while there is time.
The speaker believes that his mistress is coy, or that she is simply feigning modesty so that the speaker will find her more alluring. The speaker admonishes her for this behavior, noting that life is limited and that he doesn't have an endless amount of time to pursue her. After all, he constantly hears "time's winged chariot" at his back, getting closer with each passing day.
The speaker then attempts to convince his mistress to join him in a speedy romance by reminding her that she won't be beautiful forever. After all, he points out, her beauty will disappear when she lies in a "marble vault" and is consumed by "worms." He tells her that it would be a waste to allow her virginity to be consumed in this way.
Thankfully, the speaker returns to more positive imagery as the poem closes, reminding his mistress that she still has her youth and her beauty. Therefore, she should join him as they chase the sun and enjoy life together. The speaker is an impatient man who blurs the lines of life and death in his attempts to convince a young woman to "tear [their] pleasures with rough strife."