Shall set the sheep - By "the sheep" are denoted, here, the righteous. The name is given to them because the sheep is an emblem of innocence and harmlessness. See John 10:7, John 10:14-16, John 10:27; Psalm 100:3; Psalm 74:1; Psalm 23:1-6.
On the right hand - The right hand is the place of honor, and denotes the situation of those who are honored, or those who are virtuous. See Ecclesiastes 10:2; Ephesians 1:20; Psalm 110:1; Acts 2:25, Acts 2:33.
The goats - The wicked. See Ezekiel 34:17.
The left - That is, the left hand. This was the place of dishonor, denoting condemnation. See Ecclesiastes 10:2.

He shall set the sheep, etc. - The right hand signifies, among the rabbins, approbation and eminence: the left hand, rejection, and disapprobation. Hence in Sohar Chadash it is said, "The right hand is given, the left also is given - to the Israelites and the Gentiles are given paradise and hell - this world, and the world to come." The right and left were emblematical of endless beatitude and endless misery among the Romans. Hence Virgil: -
Hic locus est, partes ubi se via findit in ambas,
Dextera, quae Ditis magni sub moenia tendit:
Hac iter Elysium nobis; at laeva malorum
Exercet poenas, et ad impia Tartara mittit
Aen. vi. 540
Here in two ample roads the way divides,
The right direct, our destined journey guides,
By Pluto's palace, to the Elysian plains;
The left to Tartarus, where bound in chains
Loud howl the damn'd in everlasting pains.
Pitt
Of the good and faithful servants he approves, and therefore exalts them to his glory; of the slothful and wicked he disapproves, and casts them into hell.
Sheep, which have ever been considered as the emblems of mildness, simplicity, patience, and usefulness, represent here the genuine disciples of Christ.
Goats, which are naturally quarrelsome, lascivious, and excessively ill-scented, were considered as the symbols of riotous, profane, and impure men. They here represent all who have lived and died in their sins. See Ezekiel 34:17, and Zac 10:3.

And he shall set the sheep on his right hand,.... That is, the elect of God, and true believers, such as have the grace of God truly implanted in them; the sheep the Father gave unto Christ, and made his care and charge, whom he, as the good shepherd, laid down his life for; and who know his voice in effectual calling, and follow him in the way of his ordinances and appointments; and are comparable to sheep for their meekness and innocence, their simplicity and usefulness, and their harmless and inoffensive lives, and conversations: these Christ will set on his right hand, as a token of his affection for them, and a mark of respect and honour shown them, and as a pledge of that exaltation and glory he will be about to raise them to,
But the goats on the left; that is, the foolish virgins, wicked, and slothful servants, graceless professors, who, because of the impurity of their hearts, the filthiness of their lives, and their offensiveness to Christ, are compared to goats: these he will place at his left hand, in token of his disaffection for them, as a brand of disgrace upon them, and as an intimation of that dishonour, and miserable condition they will quickly be in. These different situations plainly pre-signify how things will go with each, that one will be acquitted, and made happy, the other will be condemned, and become miserable. Agreeable to which the Jews say (c), that there is a right hand and a left hand with the Lord: they that are on the right hand, are such as have done well, and are "for absolution"; and they that are on the left hand are criminals, and are "for condemnation". Some think the allusion is to the two Scribes in the sanhedrim, who stood before the judges, one on the right hand, and the other on the left, and wrote the sentences; the one of those that were acquitted, and the other of those that were condemned (d),
(c) Jarchi in Genesis. i. 26. Kimchi in 1 Kings xxii. 19. Lex. Cabalist. p. 132. Zohar in Numb. fol. 93. 4. (d) Misn. Sanhedrin, c. 4. sect. 3. Maimon. Hilch. Sanhedrin, c. 1. sect. 9. Moses Kotsensis Mitzvot Tora pr. affirm. 97.

And he shall set the sheep on his right hand--the side of honor (1-Kings 2:19; Psalm 45:9; Psalm 110:1, &c.).
but the goats on the left--the side consequently of dishonor.

He shall set the sheep at his right hand. The sheep, who represent the righteous, are placed at the right hand, the place of honor. See Hebrews 12:2.