Rubaiyat is a common shorthand name for the collection of Persian verses known more formally as the Rubaiyat of Omar Khayyam. In fact, rubaiyat (a plural word derived from the arabic root meaning 'four') means "quatrains" in the Persian language.
Rubaiyat is also used to describe the verse form popularized in Edward Fitzgerald's translation of the same collection of verses. The rhyme scheme is AABA, an arrangement that gives the verses a lilting, musical quality:
VII
Come, fill the Cup, and in the fire of Spring
Your Winter-garment of Repentance fling:
The Bird of Time has but a little way
To flutter--and the Bird is on the Wing.
In longer poems built in Rubaiyat rhyme scheme, the convention is sometimes extended so that the unrhymed line of the current stanza becomes the rhyme for the following stanza. I.e., the scheme is extended to AABA BBCB CCDC, etc.. This is sometimes called, naturally, "interlocking rubaiyat". The structure can be made cyclical by linking the unrhymed line of the final stanza back to the first stanza: ZZAZ. These more stringent systems were not, however, used by Fitzgerald in his Rubaiyat; it would have been particularly difficult for him to achieve this effect since the order and number of stanzas in his translation were not stable.
A prime use of the interlocking rubaiyat in modern English poetry is the sublime "Stopping by Woods on a Snowy Evening" by Robert Frost.
The fact that the rubaiyat are a collection of quatrains - and may be selected and rearraged subjectively to demonstrate one interpretation or another - has led to widely differing versions.
Fitzgerald gave the Rubaiyat a distinct fatalistic spin, although it has been claimed that he softened the impact of Khayyam's nihilism and his preoccupation with the mortality and transience of all things.
The term "Rubaiyat" by itself has come to be used to describe the quatrainrhyme scheme that Fitzgerald used in his translations: AABA.