Tercets are any three lines of poetry. They can be embedded within a column of lines or stand out on their own in a single stanza. There are no rules regarding whether tercets must follow a rhyme scheme or a certain meter. However, many poetic forms that make use of tercets also employ rhyme, because lines of three make excellent "envelopes" of sound; the first and final line might sound alike, while the line sandwiched within remains unique.
The Logic Behind Tercets
One famed American poet who wrote at length about the appeal of the tercet was William Carlos Williams. Williams, who wrote most of his poetry during the first third of the 20th century, felt strongly that poetry should be written with some organizing principle in mind. This was likely a response to the growing popularity of "free verse" poetry, which Williams believed was rather aimless. To compose verse that carried a precise rhythmic pace -- like waves crashing onto a beach -- Williams relied on tercets, which he believed helped the sounds within his poetry to become more measured and natural.
A popular version of the three-line form, known as an enclosed tercet, follows an "aba" rhyme scheme, with each letter standing in for an end-rhyme. "Do not go gentle into that good night,/Old age should burn and rave at close of day;/Rage, rage against the dying of the light." In this tercet by Dylan Thomas, both "night" and "light" sound alike, making them the "a" rhyme. This leaves "day" as the "b" rhyme.
Sometimes, entire poems are composed of a single tercet. English has variations on haiku, a traditional form of Japanese poetry that often emphasizes images of the outdoors or the changing seasons. Though not absolutely necessary, many poets adhere to a specified syllable-count for each line -- five in the first and final lines, and seven in the second. An excerpt from a series of haiku written by American poet Etheridge Knight reads: "Eastern guard tower/glints in sunset; convicts rest/like lizards on rocks."
Longer poems, of course, may also use tercets as building blocks, with end-rhymes forming links between each stanza. The terza rima form, for example, follows the rhyme scheme "aba bcb cdc ded" and so on, with white space standing in for stanza breaks between tercets.