What is the significance of the allegory of Hagar and Sarah in Galatians?

In Galatians 4:21-31, Paul uses the allegory of Hagar and Sarah to illustrate the two covenants. Hagar represents the old covenant, based on the law, which leads to bondage, while Sarah represents the new covenant of grace, leading to freedom and the promise of God. This distinction is crucial for understanding the Christian's position; believers are not to live under the condemnation of the law but to embrace the freedom that comes from being children of the promise through faith in Christ. The significance lies in the assurance that, through Christ, they have been given a new identity and inheritance, liberated from the law's demands.