What Does The Inerrancy Of The Bible Mean?

 The word inerrant means without error.  So a Biblical inerrantist holds that the Bible is without error.  It means the Bible is without error in the original autographs (original writings), not that all manuscripts and translations are without error.  

The Bible is inerrant because it is breathed out by God (2 Timothy 3:16).  God only speaks truth because he is the truth.  No lie or falsehood is found with him.  Biblical inerrantists believe the Bible is without error in all that it speaks to, including the areas of history and science. 

Matthew 1:21 (Short Commentary)

 (Matthew 1:21)"She will bear a son, and you shall call his name Jesus, for he will save his people from their sins."  (ESV)

The name Jesus means the Lord saves.  Jesus did not just make salvation possible, he actually saved his people from their sins.  Christ accomplished salvation for the elect.  Salvation is the work of God alone.