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
psa 8:1Upon [or according to the] Gittith, probably means that the musical performance was directed to be according to a tune of that name; which, derived from Gath, a "wine-press," denotes a tune (used in connection with gathering the vintage) of a joyous character. All the Psalms to which this term is prefixed [Psa 8:1; Psa 81:1; Psa 84:1] are of such a character. The Psalmist gives vent to his admiration of God's manifested perfections, by celebrating His condescending and beneficent providence to man as evinced by the position of the race, as originally created and assigned a dominion over the works of His hands. (Psa 8:1-9)
thy name--perfections (Psa 5:11; Psa 7:17).
who hast set--literally, "which set Thou Thy glory," &c., or "which glory of Thine set Thou," &c., that is, make it more conspicuous as if earth were too small a theater for its display. A similar exposition suits the usual rendering.
psa 8:2So manifest are God's perfections, that by very weak instruments He conclusively sets forth His praise. Infants are not only wonderful illustrations of God's power and skill, in their physical constitution, instincts, and early developed intelligence, but also in their spontaneous admiration of God's works, by which they put to shame--
still--or, silence men who rail and cavil against God. A special illustration of the passage is afforded in Mat 21:16, when our Saviour stilled the cavillers by quoting these words; for the glories with which God invested His incarnate Son, even in His humiliation, constitute a most wonderful display of the perfections of His wisdom, love, and power. In view of the scope of Psa 8:4-8 (see below), this quotation by our Saviour may be regarded as an exposition of the prophetical character of the words.
sucklings--among the Hebrews were probably of an age to speak (compare Sa1 1:22-24; Mar 7:27).
ordained--founded, or prepared, and perfected, which occurs in Mat 21:16; taken from the Septuagint, has the same meaning.
strength--In the quotation in the New Testament, praise occurs as the consequence or effect put for the cause (compare Psa 118:14).
avenger--as in Psa 44:16; one desirous of revenge, disposed to be quarrelsome, and so apt to cavil against God's government.
psa 8:3The allusion to the magnificence of the visible heavens is introduced for the purpose of illustrating God's condescension, who, though the mighty Creator of these glorious worlds of light, makes man the object of regard and recipient of favor.
psa 8:4man--literally, "frail man," an allusion to his essential infirmity.
son of man--only varies the form of speech.
visitest--in favor (Psa 65:10). This favor is now more fully illustrated.
psa 8:5God has placed man next in dignity to angels, and but a little lower, and has crowned him with the empire of the world.
glory and honour--are the attributes of royal dignity (Psa 21:5; Psa 45:3). The position assigned man is that described (Gen 1:26-28) as belonging to Adam, in his original condition, the terms employed in detailing the subjects of man's dominion corresponding with those there used. In a modified sense, in his present fallen state, man is still invested with some remains of this original dominion. It is very evident, however, by the apostle's inspired expositions (Heb 2:6-8; Co1 15:27-28) that the language here employed finds its fulfilment only in the final exaltation of Christ's human nature. There is no limit to the "all things" mentioned, God only excepted, who "puts all things under." Man, in the person and glorious destiny of Jesus of Nazareth, the second Adam, the head and representative of the race, will not only be restored to his original position, but exalted far beyond it. "The last enemy, death," through fear of which, man, in his present estate, is "all his lifetime in bondage" [Heb 2:15], "shall be destroyed" [Co1 15:26]. Then all things will have been put under his feet, "principalities and powers being made subject to him" [Pe1 3:22]. This view, so far from being alien from the scope of the passage, is more consistent than any other; for man as a race cannot well be conceived to have a higher honor put upon him than to be thus exalted in the person and destiny of Jesus of Nazareth. And at the same time, by no other of His glorious manifestations has God more illustriously declared those attributes which distinguish His name than in the scheme of redemption, of which this economy forms such an important and essential feature. In the generic import of the language, as describing man's present relation to the works of God's hands, it may be regarded as typical, thus allowing not only the usual application, but also this higher sense which the inspired writers of the New Testament have assigned it.
psa 8:9Appropriately, the writer closes this brief but pregnant and sublime song of praise with the terms of admiration with which it was opened.