What does John 12:20 mean?

Jesus is in Jerusalem for Passover. This is one of the festivals for which Jewish men are required to make a pilgrimage to the city (Deuteronomy 16:16). That has resulted in Jerusalem being packed with visitors, many of whom celebrated Jesus as He entered the city on a donkey (John 12:12–19). Not all of those visiting are ethnic Jews, however. Some of those who have come to celebrate Passover are Gentiles, who nonetheless honor the God of Israel. In this era, the term "Greeks" was used as a generic term for non-Israelites (John 7:35; Romans 1:14; 1 Corinthians 10:32; Galatians 3:28).

John does not say whether the men mentioned in this verse are God-worshippers. That seems likely, especially since there would have been little reason for them to try to speak to Jesus otherwise.

Scripture also does not specify why the men approached Philip, rather than someone else (John 12:21). They might have chosen him due to his Greek name. Or, it might have been because he knew some of them from Bethsaida. It's also possible they had no choice, and Philip was acting as the first layer of security screening for Jesus. Local religious leaders are secretly plotting Jesus' death (John 11:53), but only the details are secret. There's no question in anyone's mind that they mean Him harm (John 10:39–40; 11:8).