A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
num 24:1BALAAM FORETELLS ISRAEL'S HAPPINESS. (Num. 24:1-25)
to seek for--that is, to use enchantments. His experience on the two former occasions [Num 23:3, Num 23:15] had taught him that these superstitious accompaniments of his worship were useless, and therefore he now simply looked towards the camp of Israel, either with a secret design to curse them, or to await the divine afflatus.
num 24:2he saw Israel abiding in his tents according to their tribes--that is, in the orderly distribution of the camp (Num. 2:1-34).
the spirit of God came upon him--Before the regular ministry of the prophets was instituted, God made use of various persons as the instruments through whom He revealed His will, and Balaam was one of these (Deu 23:5).
num 24:3the man whose eyes are open--that is, a seer (Sa1 9:9), a prophet, to whom the visioned future was disclosed--sometimes when falling into a sleep (Gen 15:12-15), frequently into "a trance."
num 24:5How goodly are thy tents, . . . O Israel!--a fine burst of admiration, expressed in highly poetical strains. All travellers describe the beauty which the circular area of Bedouin tents impart to the desert. How impressive, then, must have been the view, as seen from the heights of Abarim, of the immense camp of Israel extended over the subjacent plains.
num 24:6As the valleys--Hebrew, "brooks," the watercourses of the mountains.
lign aloes--an aromatic shrub on the banks of his native Euphrates, the conical form of which suggested an apt resemblance to a tent. The redundant imagery of these verses depicts the humble origin, rapid progress, and prosperity of Israel.
num 24:7his king shall be higher than Agag--The Amalekites were then the most powerful of all the desert tribes, and "Agag" a title common to their kings.
num 24:10Balak's anger was kindled against Balaam, and he smote his hands together--The "smiting of the hands together" is, among Oriental people, an indication of the most violent rage (see Eze 21:17; Eze 22:13) and ignominious dismissal.
num 24:15he took his parable--or prophecy, uttered in a poetical style.
num 24:17I shall see him--rather, "I do see" or "I have seen him"--a prophetic sight, like that of Abraham (Joh 8:56).
him--that is, Israel.
there shall come a Star out of Jacob, and a Sceptre shall rise out of Israel--This imagery, in the hieroglyphic language of the East, denotes some eminent ruler--primarily David; but secondarily and pre-eminently, the Messiah (see on Gen 49:10).
corners--border, often used for a whole country (Exo 8:2; Psa 74:17).
children of Sheth--some prince of Moab; or, according to some, "the children of the East."
num 24:18Edom shall be a possession--This prophecy was accomplished by David (Sa2 8:14).
Seir--seen in the south, and poetically used for Edom. The double conquest of Moab and Edom is alluded to (Psa 60:8; Psa 108:9).
num 24:19Out of Jacob shall come he that shall have dominion--David, and particularly Christ.
that remaineth of the city--those who flee from the field to fortified places (Psa 60:9).
num 24:20Amalek . . . his latter end shall be that he perish for ever--Their territory was seen at the remote extremity of the desert. (See on Exo 17:13; also 1Sa. 15:1-35).
num 24:21Kenites . . . nest in a rock--Though securely established among the clefts in the high rocks of En-gedi towards the west, they should be gradually reduced by a succession of enemies till the Assyrian invader carried them into captivity (Jdg 1:16; Jdg 4:11, Jdg 4:16-17; also Kg2 15:29; Kg2 17:6).
num 24:23who shall live when God doeth this!--Few shall escape the desolation that shall send a Nebuchadnezzar to scourge all those regions.
num 24:24Chittim--the countries lying on the Mediterranean, particularly Greece and Italy (Dan 11:29-30). The Assyrians were themselves to be overthrown--first, by the Greeks under Alexander the Great and his successors; secondly, by the Romans.
Eber--the posterity of the Hebrews (Gen 10:24).
he also shall perish--that is, the conqueror of Asher and Eber, namely, the Greek and Roman empires.
num 24:25Balaam rose up, and went . . . to his place--Mesopotamia, to which, however, he did not return. (See on Num 31:8).