Hebrews 3:16-19 meaning

God had told the Israelites to enter the Promised Land, but they did not believe that God would protect them and give them the land, so they refused to enter. Because of this, God swore that those who were disobedient would not enter His rest. Enter His rest refers to receiving the full reward of the work to be done; God did not rest from creation until the seventh day, and He only rested then because all was accomplished (Genesis 2:3).

The first generation who did not believe God and hardened their hearts suffered the consequence of wandering in the desert for forty years. For who provoked Him when they had heard? Indeed, did not all those who came out of Egypt led by Moses? And with whom was He angry for forty years? Was it not with those who sinned, whose bodies fell in the wilderness? (vv 16-17). 

The first generation of Israel who came out of Egypt led by Moses died in the desert and were never able to enter and possess the Promised Land (Numbers 14:22-23). This is because God was angry for forty years, referring to the time they spent in the wilderness until every male of fighting age who refused to enter the land was deceased (Deuteronomy 2:16). 

The emphasis is that these who did not finish their task did not possess the inheritance of possessing the land. They were still God's people, and He provided for them (Deuteronomy 2:7). However, they did not possess the inheritance of the land—they did not enter God's rest.

And to whom did He swear that they would not enter His rest, but to those who were disobedient? So we see they were not able to enter [the rest] because of unbelief (vv 18-19); that is to say they did not complete the work of possessing the land so they were not able to enter the land. The reason they were not allowed to enter the land was because of unbelief. God had promised He would give them the power to overcome the walled cities and warriors of Canaan, but the Israelites refused to believe and enter the land. By refusing to enter, they were disobedient to God's commands. 

Therefore, since the first generation was disobedient, they did not gain the benefits that come with finishing the job God gave them to do. 

By application to believers today, if we question, doubt, and rebel against God, we are in danger of losing our reward that only comes through faithful obedience. Lack of belief in God is the reason that these Israelites did not enter the land. Our lack of belief in God could cause us not to enter His rest, meaning gain the reward of our inheritance. We gain the reward of our inheritance by doing everything we do in a manner that pleases God (Colossians 3:23). 

In Hebrews, the primary inheritance emphasized is to be a "son" along with Jesus, reigning the earth in harmony with Him (Hebrews 2:9-10). 

When we believe on Jesus we are made a new creation in Christ (2 Corinthians 2:17). This work is finished. Just as God rested from creating the world, being born again is a finished work. But there remains another "rest" for God's people (Hebrews 4:8-9). 

The remaining rest is the rest spoken of here. It refers to possessing the inheritance God grants to each believer. It refers to God's reward for faithful obedience. If the Israelites had been obedient to God, they would have possessed the inheritance they had been granted—the Promised Land. If we are faithful to God, we will gain our full reward (Revelation 3:21). Scripture indicates rewards can be lost in part or in whole (2 Corinthians 5:10; 2 John 1:8). 

The fact that the Pauline Author is making such an emphasis about possessing our inheritance tells us what an enormous consequence it is. We tend to think that just getting into heaven will be reward enough. It is clear from these passages that the reward of the inheritance is something that is quite enormous—something so great that we should be willing to set aside all else in this life to gain it. When we get to Chapter 12, it will be emphasized that this is exactly the mindset Jesus had, and we are exhorted to follow His example (Hebrews 12:1-2). 

The reward of our inheritance is like the great treasure of the old stories that heroic characters risked their lives to possess (1 Corinthians 2:9). Those stories all point in a very weak way to the greatest hero of all: Jesus. Jesus gave up everything to do the will of His Father, and in doing so gained the inheritance of the world (Matthew 13:44, 28:18; Philippians 2:5-9; Hebrews 2:9; Revelation 3:21). Jesus has promised to share that inheritance with all who believe, if we are willing to possess it.