Not liable to fail, deceive, or disappoint; indubitable; sure; certain; as, infallible evidence; infallible success; an infallible remedy.
When applied to a sacred text like the Bible, infallible means that the text is fully trustworthy. i.e. it does not deceive the reader into falsehood. There are problems with this concept, because even within the conservative wing of Christianity, Bible experts reach many different conclusions about divorce, hell, the millennium, Book of Revelation, and creation/evolution, etc. Since these theologians' beliefs are mutually exclusive, most must be wrong. Since they were all derived from the Bible, the concept of biblical infallibility is suspect. Within the Roman Catholic Church, the belief that the pope can speak on matters of faith and morals without error. This belief was promulgated in 1870. The pope stripped Hans Kü ng of his credentials as a teacher of Catholic theology, largely because of his questioning of the doctrine of Papal infallibility.