Hebrews 2:5-8 meaning

The Pauline Author notes that God has not given the rulership of the coming earthly kingdom to angels, nor did He give them authority over the present world: For He did not subject to angels the world to come, concerning which we are speaking (v 5). 

Genesis tells us God gave authority over the present earth to man (Genesis 1:26-28). The Pauline Author quotes Psalm 8:4-6 to show this, where David reflects on how incredible it is that the God of the universe remembers or is concerned about humankind:

But one has testified somewhere, saying,
"What is man, that You remember him?
Or the son of man, that You are concerned about him? (v 6).

This is a quote of Psalm 8:4. 

We are lowly creations, weak and insignificant compared to the heavenly beings, angels. In Psalm 8:2, humans are called "infants and nursing babes" to contrast our newness, dependence and inferior power relative to the angelic beings. And yet God (incredibly) chose to place humans over His original creation.

David muses, in spite of man's lowliness,
"You have made him for a little while lower than the angels;
You have crowned him with glory and honor,
And have appointed him over the works of Your hands;
You have put all things in subjection under his feet" (vv 7-8). 

This is a quote of Psalm 8:5-6, continuing the quote of Psalm 8:4 that began in verse 6. That humans were made lower than the angels only for a little while infers that humans were designed to eventually be elevated above the angels. But in spite of humans being initially inferior to angels, nevertheless God crowned him with the glory and honor of being appointed to reign over the earth. To be crowned is to be granted authority. In this case, God granted the authority to Adam and Eve to reign over the earth (Genesis 1:26-28). 

Humanity was given the earth to rule over. To be elevated to the status of reigning over the earth is to be given glory and honor. It is an immense honor to be granted great authority (crowned). We experience that to some extent when we see the inauguration of an elected official or the crowning of a new monarch. The festivities are glorious, to reflect the great honor being bestowed—to be granted great authority. 

Humans were appointed by God over the works of his hands. This began with Adam and Eve. 

God created Adam in His image, and created Eve to be his helper. Then God gave them an incredible responsibility: to care for and rule over every living thing on earth (Genesis 1:26). Adam was intended to take charge as a "son" (i.e., God trusting Adam to care for His creation), but he squandered that opportunity when he showed that he was not willing to walk in obedience (Genesis 3:6-7). 

The original design was not for Adam to struggle against anything in God's creation. There was supposed to be peace and harmony between everything in nature. We see this in Psalm 8 which asserts that humans were supposed to reign over:

"All sheep and oxen,
And also the beasts of the field,
The birds of the heavens and the fish of the sea,
Whatever passes through the paths of the seas."
(Psalm 8:7-8)

This is what God designed. It is how things are supposed to be. But verse 8 plainly states that things are not functioning according to God's (good) design—the way that God intended: For in subjecting all things to him, He left nothing that is not subject to him. But now we do not yet see all things subjected to him (v 8). 

Humans were supposed to rule over all, as God left nothing that is not subject to humans in His original design. However, that is not our current state. In possibly the greatest understatement in all scripture, the author writes: we do not yet see all things subjected to humans. We are supposed to be reigning over the earth in harmony with God, and in service with one another. Reality is far from that; the earth is filled with misery and violence. 

This is all due to the Fall; because Satan entered the Garden of Eden and deceived Eve and Adam, and they chose to rebel against God (Genesis 3). Through this act of disobedience, the world does not work as God originally designed. Man does not fully govern the world in harmony with God, nature, and one another. Rather, sin and death abound. 

Satan, the Enemy (Psalm 8:2), is now in charge of the world, rather than man (John 12:31). Satan delights in chaos, disharmony, and destruction (John 8:44). Our consistent companion is not peace on earth. We are a world at odds with each other and our Creator.

The Pauline Author's point here is that humans were originally given the world to rule in harmony, and yet we do not truly rule over the earth the way God intended. We do not yet see all things subjected to him (man), we are still (to varying degrees) under the power of death and Satan, and do not live the way God designed for us.

However, the word yet is vital. We do not yet see all things subjected to humans. In the word yet is embedded the amazing promise that the world will be redeemed to its original design. And that will include restoring humanity as its ruler, under the headship of Jesus, the God-man. But as we will learn, the reward of restoration to ruling is a reward that will be reserved for those believers who follow Jesus in His suffering. 

Jesus provided salvation of humans from separation from God. That salvation is received solely through faith—enough faith to look (John 3:14-15). The book of Hebrews emphasizes another salvation; Jesus has delivered humanity from the futility of having lost their designed purpose—to reign in harmony with God and one another. It is this latter salvation that we can neglect if we do not walk in full obedience to Jesus. The resulting loss will be as grim as was the loss to Israel's first generation out of Egypt when they were denied entering the Promised Land.