Hebrews 6:1 calls one foundation of salvation "repentance from dead works." Repentance means "a change of mind." Repentance from dead works means you change your mind about dead works working, ie you don't live under the law.
Hebrews 6:4-6 says, "In the case of those who have once been enlightened and have tasted of the heavenly gift and have been made partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, and then have fallen away, it is impossible to renew them again to repentance (changing their minds), since they again crucify to themselves the Son of God and put Him to open shame."
What do they "fall away" from? Grace. Paul said falling from grace was seeking to be justified by law. "You have been severed from Christ, you who are seeking to be justified by law; you have fallen from grace" (Galatians 5:4).
The NET translation notes that the crucifying & putting in Hebrews 6:6 can be understood as temporal which gives us this meaning.
"It is impossible to renew them again to change their minds WHILE they are crucifying the Son of God for themselves all over again & WHILE they are putting Him to open shame."
Galatians 5 tackles this very thing. WHILE you are seeking to be justified by law you "have fallen away" you "have fallen from grace." When you give up on being justified by the law, as Paul tried to convince the Galatians to do, you will then be able to change your mind back to grace because you trust that the one time sacrifice of Jesus has taken care of everything. Hebrews 10 makes it clear that Christ only had to die once & that any physical sacrifice is worthless because Christ's did the job. Hebrews 6 addresses something almost identical except instead of talking about living by the law in terms of physical sacrifice rituals it regards living by the law in terms of "dead works." Hebrews 6 starts off saying "we'll stop laying the foundation of repentance from dead works.. IF God permits." God didn't permit it because the very next thing spoken of in v4-8 regards repentance from dead works. To summarize, it says that as long as you trust in dead works working you'll never change your mind about trying to be justified by the law. It is a sense of "until you know it is broke it is impossible to fix it."
This is why Hebrews focuses on the perfect sacrifice of Christ. It aims to show that we have no need to recrucify Him or offer animal sacrifices anymore. But we do have to leave the old covenant behind for us to benefit from God's grace. That is the same thing Galatians 5 says, putting yourself under the law makes you "severed from Christ." This is not severed in the sense of being separated from His love, we know that is impossible. "Fallen from grace" isn't a spiritual state, it is a mental & experiential state. You cannot benefit from grace experientially while you are living under the law. The two mindsets can't coexist.
Hebrews 6:7-8 goes on to say, "Ground that drinks the rain which often falls on it and brings forth vegetation useful to those for whose sake it is also tilled, receives a blessing from God; but if it yields thorns and thistles, it is worthless and close to being cursed, and it ends up being burned."
Now lets interpret this considering the context, "Ground (a person) that drinks the rain which often falls on it and brings forth vegetation useful to those for whose sake it is also tilled, receives a blessing from God; but if the vegetation yields thorns and thistles, the vegetation is worthless and the ground is CLOSE to being cursed, and the vegetation with thorns & thistles ends up being burned."
Why is the ground only CLOSE to being burned? Because it is living under "the curse of the law" but Jesus "became a curse for us" preventing the ground from being cursed. This is teaching something similar to 1 Corinthians 3:10-15 which speaks about men's works being burned up. In that text there are good works made of gold & the like which "build upon the foundation of Jesus Christ" then there are bad works (works that misrepresent God, such as works done for the law rather than by God) made of wood, hay, & straw that are eventually burned up. To summarize Hebrews 6:7-8 is saying that those who have fallen from grace produce thorns & thistles, living under the law experiencing life as though they are cursed. But they are not cursed instead their thorns & thistles (bad/legalistic works) are burned up while they are "kept safe" though their works go up in flames. [Visit this post for a full look at 1 Corinthians 3:10-15's take on this].
Some use these verses from Hebrews 6 to teach that Christians can lose their salvation. Others, who don't believe in loss of salvation teach that these verses mean a Christian can "voluntarily choose to reject God." Neither is true, this text is about "repentance from dead works" meaning the law. The law's works cannot produce life. John 5:24 says, "Whoever trusts in the Father has eternal life and WILL NEVER be condemned; that person HAS CROSSED over from death to life." How can God extinguish ETERNAL life? He can't. God will never condemn His children even if they try to willingly, knowingly, voluntarily reject Him. God will not abort His children & you can't commit spiritual suicide, God will not allow it. We are His forever but this life on earth is infinitely better lived by grace than by law & that's what these scriptures are about. Romans 8 says "No created thing can separate us from God's love," we are created things. We cannot pluck ourselves from God's hand. God is love, if you can't be separated from his love you can't be separated from Him. If we are faithless He is still faithful.
Why Be Afraid of Hebrews 10?
Saved Through Fire? (Linked above)
Inseparable & Unforsakable, Fellowship Never Broken