But when the fullness of time had come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. (Gal 4:4-5)In these verses we can see that Paul makes a special point of saying that Christ was born under the law, in order that we who are also under the law might be redeemed. In chapter three of the same book, Paul tells us what it means to be under the law;
...For all who rely on works of the law are under a curse; for it is written, "Cursed be everyone who does not abide by all things written in the Book of the Law, and do them." Now it is evident that no one is justified before God by the law, for "The righteous shall live by faith." But the law is not of faith, rather "The one who does them shall live by them." (Gal 3:10-12)Being under the law means being governed by the law. Without obeying the law there is no life. Clearly all have broken the law.
It is for this reason then that Christ was born 'under the law'. He was born to fulfill the requirements of the law for us.
By meeting the requirements of that law, He is a worthy sacrifice to deliver us from curse of the law by undergoing the curse, and to make us heirs of the promises.
On the other hand, without that active obedience, we have no worthy sacrifice to deliver us from the curse, nor do we have the adoption as sons, by which we are given access to the heavens.