Besides being the second reading for the first Sunday of Christmas, this passage is assigned for "The Feast of Mary, Mother of Our Lord" on August 15th.
For those who may have missed Mary's feast day or any who are inclined to take this lesson as an opportunity for a meditation on Mary, feel free. After all, a church council meeting in Ephesus in 431 A.D. considered this passage (and others) in its theological deliberations regarding Mary. The consensus reached by this Third Ecumenical Council was that Mary is properly called theotokos (Greek for "God-bearer") rather than "merely" chrisotokos ("Christ-bearer"). In fact, you might offer a spell-binding sermon on the intricacies of the early Christological debates and how, in the fourth century, a bishop named Nestorius taught that Mary gave birth to the human Jesus but not to the divine logos, and how another bishop, Cyril, led the charge to keep the human and divine natures united within Mary's womb. You could do that.
On the other hand, it is likely that the Apostle Paul did not have the fight against Nestorianism and the consensus regarding Christ's "hypostatic union" in mind when he wrote "born of a woman." In fact, when the entire passage is considered, we see that it is less about the relationship of Christ's humanity and divinity, and more about the believer's relationship with God through Christ.
In the previous chapter, Paul, preaching to those Galatian believers and explained that those "under the law" (that is, everyone) cannot receive the divine inheritance through obedience to the law. Instead, the law is like a task master or disciplinarian (Greek: paidagôgos). Under the law, we have no rights before God and, therefore, we are as slaves in God's household (3:19-24). Then Paul begins to announce the promise. Now, that faith has come, we are no longer slaves serving a tough taskmaster (the law). Instead, we are God's children through faith in Christ Jesus.
In chapter four, Paul is simply underscoring his main point. Christ has come in the flesh (born of a woman!) to free us from that old master (the law), making possible our adoption as members of God's household--with all the benefits that go with it. It is no longer our relationship to the taskmaster (the law) that determines our situation in the divine household. Instead, it is our relationship to Christ (the rightful Son and heir) that determines our new status in the family. Consequently, as adopted sons and daughters, we do what children do (call their father Abba--"Daddy" for instance) and receive what children receive: blessing and inheritance.
Paul's overriding concern in the Galatians letter is the distinction between one's relationship to God through faith in Christ as opposed to one's relationship to God via the legal code. In chapters two and three of Galatians, Paul emphasizes this difference between "law and gospel" in a number of different ways. In fact, if you want to emphasize Paul's emphasis to your hearers, simply quote the source:
In chapter four, Paul illustrates the law/gospel difference in the language of relationship. Look, says Paul (in short), you cannot have it both ways. Either you are child of God because you are "under Christ" through faith, or you are slave because you are "under the law," relating to God through the law. Further on in the chapter, Paul describes the law/gospel divide in familial terms, using the child of the slave woman, Hagar, and the child of the rightful wife, Sarah, as allegories for his law/gospel distinction.
Martin Luther held in high regard the importance of distinguishing law from gospel. For Luther, in fact, only the one who could discern law and gospel could call herself a theologian. Luther wrote: "Nearly the entire Scripture and the understanding of all theology hangs on the right understanding of law and gospel." He also wrote: "Whoever knows well how to distinguish the gospel from the law should give thanks to God and know that he is a real theologian."1
Perhaps you think this law/gospel business is too theological, too abstract, for your hearers. You are probably correct. Preaching about law and gospel is one thing--a theological and abstract thing. On the other hand, doing law and gospel for your hearers is another thing all together. In the case of the passage in question--Galatians 4:4-7--this will mean proclaiming in concrete and relevant terms the difference between being a slave "under the law" and being a child, an heir, through faith.
In Paul's Galatians letter, the concrete and relevant terms had to do with circumcision. Paul "did the law" to those Galatians by testifying "to every man who lets himself be circumcised that he is obliged to obey the entire law" (5:2) and "you who want to be justified by the law have cut yourselves off from Christ; you have fallen away from grace" (5:4). Obviously, preaching on circumcision no longer cuts it--especially if you are seeking to be inclusive. Therefore, where Paul said: "If you let yourselves be circumcised, Christ will be of no benefit to you" (5:2), you will have to fill in the blank: "If you [blank] in order to gain God's blessing and inheritance, Christ will be of no benefit to you."
Fortunately, there is no shortage of things we think we can do to make God accept us into the household of Christ: be good people, go to church, assent to the creeds, give our hearts to Jesus, and on and on and on. Here the task is anything but abstract. You expose all of the subtle and not-so-subtle ways your hearers attempt to gain the divine inheritance via obedience to the law. Then you tell them, "Good luck with that." Then you hit them with the sweet gospel: "God sent his Son, born of a woman, born under the law, in order to redeem those who were under the law, so that we might receive adoption as children."
1WA 7:502.34-35 (my translation) and LW 26:115.