Biblical Inerrancy allows for contradictions in historical and scientific information that can be overlooked because of the overall spiritual significance of Scripture. Believing in it would essentially mean that you acknowledge certain textual errors but believe that because scripture is inspired by God, these errors are not as significant as the overall message.
My understanding of Inerrancy is the opposite. Biblical inerrancy is the belief that the Bible does NOT have any error or contradiction, including in historical and scientific information.
Inerrancy is something that Christians in good faith can disagree on, but this does not mean that it's an unimportant topic; it's something that needs to be seriously considered.
The word "inerrant" means "without error," and so a basic definition of biblical inerrancy would be that the bible does not contain any errors. As theologians have wrestled through this question over the past 2000 years, the general view is that the bible does not contain any errors of fact (i.e. historical, scientific, etc), and is internally consistent. This does not mean that the bible is always easy to understand, or that there aren't texts that appear to be in conflict. Nor does it mean that it's always easy to square the bible with another field of knowledge, like the natural sciences. The need for Christians to have appropriate skills in biblical interpretation (hermeneutics) is very high. What appear to be contradictions can be, with the help of interpretation tools, cleared away. Christians also need to know how to rightly relate scripture with other disciplines. In all of this, we need a heavy dose of humility and we need to be willing to have our interpretations challenged and refined as we seek God's truth in scripture and nature.
The question of inerrancy is as much about God's trustworthiness as it is about the bible's, because the bible is described as being the very Word of God. What we believe about the bible can impact what we believe about the God who speaks. As Augustine of Hippo prayed in his famous book Confessions: "Lord, surely your Scripture is true, for you, being truthful and Truth itself, have produced it.”