The speaker in "To His Coy Mistress" is trying to persuade the woman he's addressing to stop being coy—meaning specifically that she should stop being shy about sex. Even more specifically, he wants her to stop being shy about having sex with him.
In the opening lines of the poem, the speaker says that the woman's coyness wouldn't be a problem if they had all the time in the world. He says that, if they did have all the time in the world, he would gladly spend as much of that time as she wanted in wooing her. He says he would spend a "hundred years . . . to praise / (her) eyes" and "Two hundred to adore each breast." The implication is that the woman has perhaps told him that she is not ready to have sex with him, possibly because he has not proven to her yet that he really loves her. In the first stanza, the speaker tries to reassure the woman that this is not the case.
In the second stanza, the speaker says that—although he would gladly woo her and convince her of his love for years if he could—he can't because his time is finite. Indeed, he says that he can always hear "Time's wingèd chariot hurrying near." He says that if she is always so shy (or coy) about having sex with him, then eventually they will both be too old to enjoy sex anyway: her "beauty shall no more be found" and her "long-preserved virginity" will be wasted on the worms in the grave.
In the third stanza, the speaker tries to convince the woman that they should take advantage of their youth before time—their common enemy—takes it away from them. He frames her coyness as an "affront" to (or a waste of) their youth, as well as a surrender to "the slow-chapped power" of time.
This poem was written in the seventeenth century when a woman was expected to preserve her virginity until she was married. A woman who had sex before or outside of marriage was considered a "fallen woman"—or an outcast who was no longer fit for marriage. In this context, the coyness of the woman addressed in this poem therefore seems perfectly reasonable.