I wasn't sure what verse 2 meant, "Out of the mouths of babes and infants you have founded a bulwark because of your foes, to silence the enemy and the avenger," so I turned to several commentaries. Among them was The Book of Psalms, A Translation with Commentary, by Robert Alter.
He says that the phrase "mouths of babes and sucklings [his translation] does not have a clear meaning and has never been satisfactorily explained. He supplies what he terms a distant possibility:
God draws strength from consciously aware humankind, made in His image, even from its weakest and youngest members, against the inhuman forces of chaos. Perhaps the innocence of infants is imagined as a source of strength.
Psalm 8 begins with an assertion of the greatness of God, Master of the earth. This powerful, majestic God turns to the weakest among us to put an end to threats. Alter says:
Because this is a psalm celebrating creation, there is plausibility in the identification proposed by some scholars between this implacable foe and the primordial sea monster, who, in Canaanite myth, must be subdued by the god of order so that the world can come into stable being Imagery taken from that cosmogonic battle between gods is borrowed by a good many psalms.