Why is the concept of righteousness by faith significant in Christianity?

The Apostle Paul in Romans 4:13 teaches that the promise of being heirs is through the righteousness of faith, not through the law. This is significant for Christianity because it emphasizes that salvation is entirely a work of God's grace, received through faith. Believers cannot achieve righteousness through their own works or adherence to the law, making it critical to understand that faith is the conduit through which God's grace flows. This foundational truth demonstrates that human efforts, no matter how sincere or noble, fall short of God’s requirement for righteousness, highlighting the necessity of Christ’s sacrificial work on behalf of sinners.