What does Matthew 15:23 mean?

Jesus has done something unusual to withdraw from the crowds and religious leaders. He has left the borders of Israel, travelling to Tyre and Sidon, east of Galilee, with His disciples. This area is not only dominated by Gentiles, it's the example Jesus used to shame Israelites for their lack of repentance (Matthew 11:20–24). Jesus knows He is much less likely to be recognized and mobbed outside of Israel, and Mark tells us that He is staying in a house and didn't want anyone to know He was there (Mark 7:24).

All the same, He is approached in the house by a Canaanite woman. She seems to know exactly who He is and what He can do for her "little daughter" (Mark 7:25), who is severely oppressed by a demon. She calls Jesus the "Son of David," suggesting she knows Him to be the Messiah of Israel. She wants Jesus to free her daughter from the demon.

At first, Jesus remains silent. In fact, He seems to ignore the woman completely, the exact opposite of His normal response to such requests (Matthew 14:35–36; 15:29–30). The woman will not take His silence for an answer, however, and continues to cry loudly. The disciples eventually lose patience and ask Jesus to send the loud woman away.

It's unclear if the disciples wanted Jesus to send her away without helping her. More likely, they wanted the Master to heal the woman's child, so she'd go away and leave them alone (Luke 18:1–8).