This Psalm is a calm interlude from the ones surrounding it which talk of the attacks and sufferings enemies are bringing.
We see the simple praise which God receives from even infants contrasted with the defiance of terrible people. Jesus quotes it in Matthew 21:16 to demonstrate the trust (or faith) infants and children have in him.
And this praise is for God’s creation in all its vast array (akin to Romans 1:20). It’s a very fitting Psalm for me today considering that yesterday at church for Trinity Sunday we focused on how in Creation God created humanity to bear his image, with the humility (8:4-5) and responsibility that this all entails in ruling over God’s world (8:6-9) in a benevolent way, the way Christ rules over the Church.
On a grammatical note, 8:2 is a bit tricky. The word for “give” or “set” has an unusual form or use. My best guess is that it’s a short form which has “your name” as the subject. So “[your name] which has placed…” The sense is clear, though, either way you take it.
And 8:6a is quoted in Hebrews 2:6-8 to support Jesus’ universal rule over all things. And the phrase could mean either, “you made him a little lower,” or “you made him lack for a little while.” And the common Hebrew word for God is occasionally used for angels, hence the way the New Testament quotes from the Septuagint wording.