"O Lord, our Lord, how majestic is your name in all the earth! You have set your glory above the heavens." NIV translation
We are reminded that the name of God is above all names as He is the Creator. He has not created everything and then just left us alone but has given us His presence (glory) as well.
"From the lips of children and infants you have ordained praise because of your enemies, to silence the foe and the avenger." NIV translation
We are reminded that it is with childlike faith that we accept God and His gift of salvation. Children do not work for what they need to survive but instead just trust in their parents. The "enemies" refers to Satan and those who reject Jesus as the Son of God. The "avenger" refers to the fact that Satan hates us and hates God because he could not replace God. The devil wants revenge by stealing what is most dear to God and that is us (His children). Satan will be silenced when Jesus returns and he is cast into Hell (see Revelation 20).
Psalm 8:3 & 4
"When I consider your heavens, the work of your fingers, the moon and the stars, which you have set in place, what is man that you are mindful of him, the son of man that you care for him?" NIV translation
We are reminded that it was really no big deal for God to create everything including the heavens as it only took His fingers. Really, as we see in Genesis 1, it didn't even take His fingers but simply His words. As people, for real work it takes not only our fingers but usually our hands and arms as well so David asks the simple question of why God cares for us. It is somewhat easier to see how God could care for Adam (man) before the fall but it is more amazing than the stars in the sky as to why God would care for the son of man (children of the fallen Adam).
"You made him a little lower than the heavenly beings and crowned him with glory and honor." NIV translation
We are reminded of the order of things and that is God above all others followed by the angels in heaven. We were created a little lower than the angels (more humble) but God has a way of elevating the humble things.
"You made him ruler over the works of your hands; you put everything under his feet: all flocks and herds, and the beasts of the field, the birds of the air, and the fish of the sea, and all that swim the paths of the seas." NIV translation
How did God elevate mankind from the humble? As we see here, God put us in control of every creature that is on this earth. There are some, today, that will elevate animals to a place above their fellow man, but, that is not how God set things up.
There are also those that mistreat animals and that is not right either as God wants us to be good rulers. Being a good ruler involves being like Jesus as He is the overall ruler of the earth and everything in it.
"O Lord, our Lord, how majestic is your name in all the earth!" NIV translation
The song ends as it began with praising God for all He has done. We can use this verse and it will help us to remember what God has done as we go through tough times just as David did.