Something that has inerrancy is completely accurate and cannot be wrong. Many Christians believe in the inerrancy of the Bible.
You're most likely to come across the noun inerrancy in a religious context. It usually describes Christian religious writing — particularly the Bible — and the word of God. People who believe in a literal interpretation of the Bible are most likely to emphasize its inerrancy. In other words, they think that everything in the Bible is the literal truth. Inerrancy comes from inerrant, which originally referred to stars in the sky, and which is rooted in inerrantem, "not wandering" in Latin.