We're about to throw a lot of poetry vocab at you, so brace yourself. "To Celia" actually has two different meters: iambic tetrameter and iambic trimeter.
Let's start with "iambic." An "iamb" is an unaccented syllable followed by an accented one. It makes a sound like da-DUM. Easy enough.
Next up is "iambic tetrameter." "Tetra" means "four" (like Tetris) and "meter" refers to a regular rhythmic pattern. So iambic tetrameter is a kind of rhythmic pattern that consists of four iambs per line. It sounds like four heartbeats:
da-DUM da-DUM da-DUM da-DUM
The odd-numbered lines are written in iambic tetrameter. Let's check out an example from the first line. We'll put slashes between the iambs and bold the stressed syllables.
Drink to | me on|ly with | thine eyes
The even-numbered lines are in a meter called iambic trimeter, which is the same as iambic tetrameter except there are three ("tri," like tricycle) iambs instead of four. Take line 2 as an example:
And I | will pledge | with mine.
"To Celia" also rhymes and has the following rhyme scheme: ABCBABCB DEFEDEFE. We'll assign letters to each rhyme in the first stanza to show you what we're talking about:
Drink to me only with thine eyes (A)
And I will pledge with mine; (B)
Or leave a kiss but in the cup, (C)
And I'll not look for wine. (B)
The thirst that from the soul doth rise (A)
Doth ask a drink divine: (B)
But might I of Jove's nectar sup (C)
I would not change for thine. (B)
Notice how the A's all rhyme (eyes, rise), the B's rhyme (mine, wine, divine, thine), and the C's rhyme (cup, sup).