Easton's Bible Dictionary 
When our Lord retired into the borderland of Tyre and Sidon ( Matthew 15:21 ), a Syro-phoenician woman came to him, and earnestly besought him, in behalf of her daughter, who was grievously afflicted with a demon. Her faith in him was severely tested by his silence ( Matthew 15:23 ), refusal (24), and seeming reproach that it was not meet to cast the children's bread to dogs (26). But it stood the test, and her petition was graciously granted, because of the greatness of her faith (28).
Morrish Bible Dictionary 
The designation of the woman whose daughter was possessed by a demon. She belonged to Phenice in Syria: the name embraced both these proper names. By birth she was a Greek, which here probably means simply 'Gentile.' Mark 7:26 . In Matthew 15:22 she is called 'a woman of Canaan.'