Free verse is poetry that does not use a fixed meter. That is, it does not use numerically-measured patterns of syllables, stresses, vowel lengths, etc.
Charles O. Hartman, in his book Free Verse: An Essay in Prosody (Princeton University Press, 1980), defines free verse by what it is not: it is not metrical. Free verse differs from metrical verse in that they use different kinds of prosody.
“Prosody,” as Hartman defines it, is a “system of rhythmic organization” by which the poet “control[s] the reader’s temporal experience of the poem, especially his attention to that experience.” Metrical prosody is a prosody that relies on a “numerical rule” – for example, in most of Shakespeare’s plays and poems, each line contains five pairs of syllables, each of which contains first an unstressed syllable and then a stressed one (though most lines actually vary from this pattern in one way or another); many of Marianne Moore’s poems follow rules about how many syllables (regardless of whether they are stressed or not) occur in each line; Old English poetry had rules about the number of stressed syllables per line, but did not count unstressed ones; and ancient Greek poetry counted patterns of long and short, rather than stressed or unstressed, syllables. In metrical poems, the poet has a vast array of techniques for “controlling the reader’s temporal experience,” including adherence to or variation from the meter, making significant words occur at significant metrical points (for instance, in a place where a stress is expected), and splitting metrical units across grammatical units such as sentences.
In free verse, though, the poet uses techniques other than a numerical rule to “control the reader’s temporal experience of the poem.” Among the most important of these are lineation, enjambment, and counterpoint – that is, choosing where to end a line; splitting sentences or phrases across lines; and creating tension between the meaning of the complete sentences of the poem and the meaning of individual lines when read as if they were complete sentences themselves. These techniques are available to the metrical poet as well, but they take on added importance in free verse because other, metrical, prosodic techniques are unavailable.
Free verse, which by definition is not metrical, should not be confused with blank verse, which is metrical (it is unrhymed iambic pentameter).