Hebrews 3:7-11 meaning

This section containing vv 7-11 is a direct quote from Psalm 95:7-11. The Psalm starts out as a call to worship and ends with a reminder of the penalty, the consequence for refusing to repent and acknowledge God, using the Israelites as an example. 

The Pauline Author is using this passage to implore his Jewish audience (who would be familiar with this psalm) to not make this mistake of hardening their hearts toward God. It is obvious from these verses that believers have a choice: we can choose to harden our hearts to God, and if we do there will be negative consequences:

Therefore, just as the Holy Spirit says,
"Today if you hear His voice,
Do not harden your hearts as when they provoked Me,
As in the day of trial in the wilderness (vv 7-8). 

These verses reference a time when Moses brought the Israelites out of slavery in Egypt and led them toward the land that God had promised so that they could take possession of it (Genesis 17:8). The land was promised to them as an inheritance. 

When they came to that land, in the day of trial in the wilderness, they were afraid of the people who dwelt there and declined God's promise that He would be with them and make them successful if they would enter and take the land. Instead they made plans to return to Egypt. Because they hardened their hearts against God and did not trust in His promises, He made them wander in the desert for forty years. 

God refers to their wandering in the wilderness as a time Where your fathers tried Me by testing Me, and saw My works for forty years (v 9). That first generation did not possess their inheritance, because they did not enter and possess the land God had granted them. Another word for inheritance is "possession." You could also say that God granted them a possession, but they failed to possess their possession.

All those who hardened their hearts against God never took possession of the land God had promised to their fathers (Numbers 14). This does not mean that the Lord rejected the Israelites from being His people. He cared for them while they wandered in the desert for 40 years, giving them food and clothing (Deuteronomy 8:3-4). 

But the disobedient first generation missed out on an inheritance of possessing the land that was set aside for them; it was theirs to possess, but they shrank back in fear. They did not possess their inheritance because they did not exercise faith that God would fulfill His promise. 

The next generation did possess that possession, believing God and acting upon His promises. In a similar way, each believer has a great inheritance prepared for them, but it must be possessed through a walk of faith (Colossians 3:23). The Pauline Author will make that point very clear. Walking in faithfulness allows us to possess our full reward (2 John 1:8). 

The Israelites who died in the wilderness were God's people. God cared for them, led them, and called them a redeemed people (Exodus 15:13). However, they did not enter His rest—meaning they did not complete the work God gave them to do (which is when we should rest) and therefore did not receive their reward for completing the job. They did not enter and possess their inheritance, which is the land God had granted them:

"Therefore I was angry with this generation,
And said, 'They always go astray in their heart,
And they did not know My ways';
As I swore in My wrath,
'They shall not enter My rest'"  (vv 10-11). 

In this case to not enter My rest means to not enter, possess, and reign over the Promised Land. After the people refused to believe God, God declared:

 "Surely all the men who have seen My glory and My signs which I performed in Egypt and in the wilderness, yet have put Me to the test these ten times and have not listened to My voice, shall by no means see the land which I swore to their fathers, nor shall any of those who spurned Me see it."
(Numbers 14:22-23)

God continued to care for His people while wandering in the wilderness, miraculously feeding them manna, and causing their clothing to not wear out (Deuteronomy 8:3-4). But they did not "enter His rest" meaning they did not possess the inheritance He had granted to them, through His promise to Abraham (Genesis 15:18). 

God declares that they did not possess the land that had been promised to their fathers because they always go astray in their heart, and they did not know My ways (v 10)—they hardened their hearts and did not believe that God's instructions were for their best. 

They had trusted God for their deliverance from Egypt—they believed God, and the angel of death passed over them when they left slavery in Egypt. But they failed to believe God would successfully lead them into Canaan. Similarly, if believers (who have been justified in the presence of God by faith) choose to harden their hearts toward God and do not obey Him, they will likewise not take possession of their inheritance. New Testament believers possess their inheritance by doing all they do in order to please God (Colossians 3:23). 

The inheritance of Israel was to possess and reign over the land God promised. The inheritance of believers-at-large is to be "crowned with glory and honor" (Hebrews 2:7-9), to be reinstated to our original design to reign over the earth in harmony with God, one another, and nature. The Apostle Paul asserted that faithfulness in all that we do to please God was the path to gaining the reward of our inheritance (Colossians 3:23).