What is rhythm, meter, and syntax?

Syntax refers to the arrangement of the words, phrases, and clauses that make up a sentence.
Meter refers to the pattern of stressed and unstressed syllables in a line of poetry. Its unit of measure is called feet. The first line of Robert Frost's "Stopping By Woods on a Snowy Evening" is: "Whose woods | these are | I think | I know." There are eight words of a single syllable in this line, and the words that are bolded are the ones that are stressed. The meter of this line is iambic tetrameter (tetrameter means there are four metrical feet, which is where the vertical divisions are, above).
Rhythm is also a function of poetry. It is created through the pattern of stressed and unstressed syllables; as this pattern emerges in successive lines and stanzas, the rhythm becomes apparent.