"In passing judgment on another you condemn yourself, because you, the judge, are doing the very same things."
In the first few chapters of Romans, Paul is contemplating possible paths to salvation. He has already concluded, in Romans 1, that God's wrath is being poured out on the world because it - in mass - has been engaging in idolatry and immorality. Sin does not lead to the Lord's blessing, but rather ends in separation from God.
In Romans 2, Paul moves on to the case of individuals (primarily Jews) who stand apart from the nations and stand back from the world's sin - and point an accusing finger at it. These are those who would take pride in their special position of having the law, believing it sufficient to save them. "Are they in any better condition?" Paul asks. "Is one route to salvation to possess the law and stand in judgment of sinners?"
No, Paul argues, because knowledge of the law doesn't necessarily mean sinlessness. You can tell others not to steal or commit adultery, yet still be guilty of it yourselves. The picture in my mind is of John 8 when Jesus invited the crowd, "Let anyone among you who is without sin be the first to throw a stone at" the woman caught in adultery. One by one they dropped their stones and left, realizing that they did not fit the criterion of being without sin.
So being a Jew instead of a Gentile doesn't matter in the eyes of God. ("For God shows no partiality" - verse 11) In fact, real "Jewishness" isn't a matter of the flesh manifested in outward circumcision at all, but of the heart, revealed in an inward circumcision toward God!
It is so important in spiritual/religious matters that our insides match our outsides. Otherwise, we run afoul of the characteristic that both Paul and Jesus equally decried: Hypocrisy.