A woman of Canaan - This woman is called, also, a Greek, a Syro-Phoenician by birth, Mark 7:26
In ancient times, the whole land, including Tyre and Sidon, was in the possession of the Canaanites, and called Canaan. The Phoenicians were descended from the Canaanites. The country, including Tyre and Sidon, was called Phoenicia, or Syro-Phoenicia. That country was taken by the Greeks under Alexander the Great, and those cities, in the time of Christ, were Greek cities. This woman was therefore a Gentile, living under the Greek government, and probably speaking the Greek language. She was by birth a Syro-Phoenician, born in that country, and descended, therefore, from the ancient Canaanites. All these names might, with propriety, be given to her.
Coasts - Regions or countries.
Thou son of David - Descendant of David. See the notes at Matthew 1:1. The phrase here means the Messiah.
Is grievously vexed with a devil - See the notes at Matthew 4:24. The woman showed great earnestness. She cried unto him, and fell at his feet, Mark 7:25.

A woman of Canaan - Matthew gives her this name because of the people from whom she sprung - the descendants of Canaan, Judges 1:31, Judges 1:32; but Mark calls her a Syrophenician, because of the country where she dwelt. The Canaanites and Phoenicians have been often confounded. This is frequently the case in the Septuagint. Compare Genesis 46:10, with Exodus 6:15, where the same person is called a Phoenician in the one place, and a Canaanite in the other. See also the same version in Exodus 16:35; Joshua 5:12.
The state of this woman is a proper emblem of the state of a sinner, deeply conscious of the misery of his soul.
Have mercy on me, etc. - How proper is this prayer for a penitent! There are many excellencies contained in it;
1. It is short;
2. humble;
3. full of faith;
4. fervent;
5. modest;
6. respectful;
7. rational;
8. relying only on the mercy of God;
9. persevering.
Can one who sees himself a slave of the devil, beg with too much earnestness to be delivered from his thraldom?
Son of David - An essential character of the true Messiah.

And, behold, a woman of (f) Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, [thou] Son of David; my daughter is grievously vexed with a devil.
(f) Of the people of the Canaanites, who dwelt in Phoenicia.

And behold a woman of Canaan,.... That is, of Phoenicia, which was called Canaan; so Shaul, the son of a Canaanitish woman, is, by the Septuagint in Exodus 6:15 called the son of a Phoenician; and the kings of Canaan are, by the same interpreters in Joshua 5:1 called kings of Phoenicia: hence this woman is by Mark said to be a Greek, that is, a Gentile, as the Jews used to call all of another nation, and a Syrophenician, being a native of Phoenicia, called Syrophenician; because it bordered upon Syria, and had been formerly a part of it, by conquest: so Cadmus, who is reported to have first brought letters from Phoenicia to Greece, is called (i) a Syrophenician merchant.
Came out of the same coasts; being an inhabitant, it is very likely, either of Tyre or Sidon: this shows that Christ did not go into these places, but only to the borders of them, since she is said to come out of them to him; who, having heard of him, and the miraculous cures wrought by him, and being informed that he was near, at such a place, as the Persic version says, "suddenly came forth out of a corner"; and the Ethiopic reads it, "out of the mountains thereof"; and made to the house where he was privately retired, and would have hid himself, as Mark suggests,
and cried unto him; with a loud voice, with much vehemency, being in great distress,
saying, have mercy on me; meaning, by curing her daughter, with whose case she was so much affected, that she made it, as it were, her own:
O Lord, thou son of David. The first of these characters expresses her faith in his power, dominion, and government, that all persons and things, and so all diseases were at his command, and control; and that being Lord of all, he could remove them at his pleasure: the other shows her knowledge and belief of him, as the Messiah, that being a name by which he was usually known by the Jews; See Gill on Matthew 1:1 and which she, though a Gentile, might come at the knowledge of, either through being a proselyte to the Jewish religion, or through a general report which might reach, especially the neighbouring nations, that the Jews expected a wonderful deliverer to arise among them, under this character of the son of David; and from what she had heard of him, she concluded he must be the person.
My daughter is grievously vexed with a devil, which had took possession of her, and most grievously afflicted her: and her request to him was, that he would cast him out of her: believing he had power so to do, without seeing or touching her, only by a word speaking: her faith was like that of the centurion's.
(i) Lucian. Dialog. Deor. Coneil. sect. 2,

Behold, a woman of Canaan. The name Canaan was the oldest bestowed upon the country, and all the heathen inhabitants were often called Canaanites, whether of the same stock or not. Mark says (Mark 7:26) that the woman was a Greek, a Syro-Phoenician; i. e., a Gentile, and a Syro-Phoenician, because she lived in the district of Syria called Phoenicia.
Have mercy on me. She has a boon to ask for her daughter, or rather indeed for herself, for so entirely had she made her daughter's misery her own.
My daughter is grievously vexed with a devil. More correctly, "a demon." See note on Matthew 8:28.
O Lord, thou son of David. It is remarkable that two of the brightest examples of faith seen in the ministry of Christ were exhibited by Gentiles, that of the centurion (Matthew 8:8-9), and of this woman. The fact that the latter addresses Jesus as "the son of David," shows that she knew of the prophecies concerning the Christ and that he would be the son of David.

A woman of Canaan - Canaan was also called Syrophenicia, as lying between Syria properly so called, and Phenicia, by the sea side. Cried to him - From afar, Thou Son of David - So she had some knowledge of the promised Messiah.