In Galatians 4:21-31 we find the apostle Paul using an allegory to teach the Galatian believers about the true nature of Israel. Paul begins by saying that the mothers of Abraham’s children, Sarah and Hagar (Keturah and her children are not mentioned in this context), represent two covenants. He is referring to the Old and the New covenants. Hagar represents the Old or Mosaic Covenant, while Sarah represents the New Covenant. Hagar is described as the slave woman, while Sarah is described as the free woman. The covenant that Hagar represents is from Mount Sinai, which represents the present city of Jerusalem, and is said to bear children who are to be slaves. This is another way of saying that the Old Covenant was a works covenant and could only produce unbelievers.
Paul goes on to describe what the New Covenant, the work of Jesus on the cross, produces, which are believers. The New Covenant is described as the Jerusalem that is above and she (Sarah) is our mother. This covenant produces true believers who have their sins forgiven and a new heart (Hebrews 10:14).
At this point in the passage Paul quotes an Old Testament verse (Isaiah 54:1) that prophetically describes a time in the future when Israel will be regathered back into the land of Palestine. This is interpreted by Paul as referring to the New Covenant era (from Pentecost until the 2nd Coming) when God will produce a real people of God (the church). This will be unlike the people produced by the Old Covenant (Israel) for they were unbelievers. They were only a temporary, unbelieving, picture of the people of God. The church is a spiritual Israel. In Isaiah 54:1 Israel is described as a desolate woman who cannot bear any children. This is an accurate appraisal of Israel under the Old Covenant who were rejected by God. This rejection is seen in the destruction of the northern kingdom in 722 BC and the destruction of the southern kingdom in AD 586. With the coming of the New Covenant era God is once again going to make Israel fertile. This fertility is seen in those coming to faith in Jesus Christ this side of Pentecost. This is a spiritual Israel and it is the church. The prophecies regarding the regathering of Israel back into the land are truly fulfilled by the coming of the New Covenant era and the church of Jesus Christ.
At this point in the passage Paul states that those produced by the Old Covenant, which is literal Israel, are persecuting those produced by the New Covenant. He then goes on to say that we (true believers) are not the children of the slave woman (Hagar=Old Covenant). We are the children of the free woman (Sarah=New Covenant). This allegory brings out into the open the truth that literal Israel was never intended to be the real people of God. They were only a temporary picture until the real people came along.