The Sibyls were oracular seeresses of antiquity who prophesied at certain holy sites, under the divine influence of a deity, originally one of the chthonic earth-goddesses.
Later in antiquity, Sibyls wandered from place to place. Plato only speaks of one Sibyl, but in the course of time the number increased to nine. To the classical sibyls of the Greeks, the Romans added a tenth. These ten were the Babylonian or Persian Sibyl, the Libyan, the Cimmerian, the Sibyl of Delphi, the Erythraean, the Samian, the Cumaean, the Hellespontine, the Phrygian and the Tiburtine. Long after the oracles had long been silenced by the Christians in the 4th century, the number of Sibyls was increased in the Middle Ages to as many as twelve.
The Sibylline Books of Roman history were a collection of oracular utterances, set out in Greek hexameters and were lost twice, thus there is very little knowledge of the actual contents. The Sibylline Books should not be confused with the so-called Sibylline Oracles. The twelve books of pseudo-Sibylline Oracles written in Greek hexameters, which have survived, contain pretended prophecies by various authors and of various dates, from the middle of the second century B.C. at the earliest, to the fifth century A.D. They were composed partly by Alexandrian Jews and revised and enriched by Christian editors, who added similar texts, all in the interests of their respective religions; and in part they refer to events of the later Roman Empire.
Sibylline language
As sibylline means characteristic of, or relating to, a sibyl or prophetess, sibylline language would be oracular and/or represent that which has a secret or hidden meaning.