I was browsing through some of the places that Psalm 8 is quoted in the BYU Citation Index, and this phrase caught my eye:
Thou madest him to have dominion over the works of thy hands; thou hast put all things under his feet. (vs. 6, emphasis added)
This phrase became even more interesting when I realized that different apostles and prophets use these verses to mean both mankind and also Christ. I love the way that the Lord layers meaning in the scriptures, and uses the same passage to teach different lessons, depending on where we are and what lessons we are in need of. Elder Monson used the Psalm to refer to mankind when he said:
David declares in one of his beautiful and moving psalms, “O Lord our Lord, how excellent is thy name in all the earth! … “When I consider thy heavens, the work of thy fingers, the moon and the stars, which thou hast ordained; “What is man, that thou art mindful of him?” (Ps. 8:1, 3–4)
Job, that righteous man of old, joined in the question when he asked, “What is man, that thou shouldest magnify him? and that thou shouldest set thine heart upon him?” (Job 7:17 )
One need not grope for answers to these penetrating questions when in your presence here in the historic Tabernacle or with you in the many meeting places throughout the world where you have assembled. “Ye are a chosen generation, a royal priesthood, an holy nation” (1 Pet. 2:9) “Ye … are … a spiritual house, an holy priesthood” (1 Peter 2:5)
But one in a certain place testified, saying, What is man, that thou art mindful of him? or the son of man, that thou visitest him?
Thou madest him a little lower than the angels; thou crownedst him with glory and honour, and didst set him over the works of thy hands:
Thou hast put all things in subjection under his feet. For in that he put all in subjection under him, he left nothing that is not put under him. But now we see not yet all things put under him.
But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.
Looking through the various places in scriptures, it looks like this phrase is predominantly used to refer to the majesty and power of Christ. And that has been a recurring theme in the Psalms I've looked at thus far.