But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God. (ESV)
When we think of what defines being a Jew we might be missing the point of what Paul is saying in this verse. We can consider people being descendants of those born in Israel. We can think of those who celebrate Hanukkah and other Jewish holidays. We can even think of the covenant that God made with Abraham that he would be the father of many nations. Abraham was the father of all the Jews.
While the Jews were very proud of their lineage a Jew is more than just a physical descendant of Abraham. Paul is saying that a true Jew is one inwardly. Being a descendant of Abraham, celebrating feasts, attempting to keep the Law, or even the physical act of circumcision does not make one a true Jew. It is a matter of the heart.
This fact of faith being a matter of the heart and not physical works is one that was lost on many Jews. Those who knew the Law were fixated on the act of keeping the Law, but in the process only proved how incapable they were. The Law is impossible to fulfill because we are human and cannot keep God's holy, perfect law.
This is why the true Jew needed to be one in their heart. They needed to have genuine faith in God and his work on their behalf. In the Old Testament the true Jews were the ones who, through the sacrificial system, looked forward to a Messiah who would ultimately fulfill the Law for them. True Jews today are those who depend on that same Messiah (Jesus) for their righteousness.
Are you a true Jew? I do not mean your physical lineage. Have you placed your faith in the Messiah, Jesus? Salvation is a matter of the heart, by God's grace, not your works.