In the first two lines of "To His Coy Mistress," the poem establishes its form and its central concern. The speaker addresses someone directly, whom he calls "Lady." (This introduces one of the poem's key devices, apostrophe: the rest of the poem will be an apostrophiac address to the Lady). His tone is familiar, teasing, and also a bit stern. Though the speaker seems to know the Lady well, he nonetheless disapproves of her choices, and wants to convince her to change, to live differently. The lady that the speaker address is the same woman mentioned in the title, "His Coy Mistress." The word "mistress" means something different now than it did in Marvell's time. Though contemporary speakers use the word to describe a woman who has an affair with a married man, Marvell uses the word in a much more general sense: it simply describes a woman who holds authority of some kind, such as a female head of household.
The reader may wonder what authority the mistress of Marvell's poem holds. It's a tricky question to answer, because the poem doesn't tell its readers much about her. In fact, at most, the reader knows that she is "coy:" she is flirtatious, but she has refused the speaker's advances. The speaker begins the poem by reproaching her for doing so. He emphasizes, though, that her reticence and delay is not a crime in and of itself: if the two "had...world enough and time" it would be perfectly acceptable. In other words, if both the speaker and the mistress were immortal, then the mistress could flirt and delay as long as she wanted to. But, the speaker implies, since they are not immortal—since they can and will die, perhaps soon—it is a "crime" to delay, to flirt, as the mistress has seemingly done in the past.
The first two lines stand as a formal unit. Each line is in flawless iambic tetrameter, and the lines rhyme with each other in an AA scheme. Further, the first line introduces a thought which the second line completes. This establishes a pattern for the poem: the speaker's thoughts often fall into two-line rhyming units, or couplets. When they do not—that is, when a thought ends halfway through the second line or continues into a third—this is a potentially significant variation in the formal structure of the poem. The poem binds together the various concepts it introduces in these opening lines through alliteration, for example using a repeated /w/ sound, which stretches into line 4. The opening lines of the poem also establish the poem's logical structure, which is a syllogism: introducing its major premise: if we had all the time in the world to love each other, you could be as coy as you want.