Sappho was an enormously influential musician and lyric poet (Plato called her "the tenth Muse") who flourished around 600 BCE on the island of Lesbos off the coast of Asia Minor. She composed in the Aeolic dialect, an eastern form of Greek that dropped the "h" sounds from the beginning of words and often used long ᾱ where Attic Greek had η. In general, Aeolic sounded more archaic, stately and musical than Attic Greek, somewhat like the English spoken in the Deep South of the United States in comparison with the standard pronunciation used in the broadcast industry.
Sappho has always been famed for her love poetry, but she was first and foremost a musician of genius, and we have it on good authority that she invented the Mixolydian mode, which modern blues and rock guitarists use for the majority of their music, in the guise of the pentatonic scale with the addition of the "blue note" or flatted fifth. So it is possible to trace a musical influence from Sappho to Led Zeppelin, traveling through Africa and Mississippi along the way.
Fragments of Sappho's poetry have come down to us along four different paths. In the first place, we have the verses that were quoted by other authors, primarily in literary handbooks written by Greek scholars during the period of classical Rome. Second, we have a single potsherd from the 3rd century BCE that was decorated with the stanzas of Fragment 2. Third, we have a scattering of papyrus fragments that were discovered just a century ago in rubbish mounds at the site of Oxyrhynchus, an ancient Hellenistic capital in Egypt. Fourth, we have papyrus fragments that were recycled as mummy casings and continue to surface on the market, since many of them belong to private collectors.
Recently, scholars have been excited by the discovery of papyrus fragments of the latter variety (purchased from a private collector by the University of Cologne in 2002) which, combined with the existing Fragment 58, yield a substantially complete poem.
Most of Sappho's poetry is still out there somewhere, waiting to be discovered or simply recognized.
Note: Anyone seriously interested in the poetry of Sappho should buy David A. Campbell's Greek Lyric Poetry, published by Bristol Classical Press, and his book Greek Lyric I: Sappho and Alcaeus, in the Loeb Classical Library. Both are readily available from online booksellers.