Therefore leaving the principles of the doctrine of Christ, let us go on unto perfection; not laying again the foundation of repentance from dead works, and of faith toward God, Of the doctrine of baptisms, and of laying on of hands, and of resurrection of the dead, and of eternal judgment. And this will we do, if God permit. For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost, And have tasted the good word of God, and the powers of the world to come, If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame. For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned.
The common approach to this text is with a presupposed question, "Does Hebrews 6 teach that a believer can lose their salvation?" The best way to answer this is to first recall how one receives salvation. Salvation is a deliverance from sin and death (the judgment of God). The very message of Jesus was to "repent and believe." In Acts 2, according to Peter, all who call on the name of the Lord shall be saved. He also added that repentance was needed. In Romans 10 Paul teaches that it is a belief of the heart and a confession of that belief acknowledging that Jesus is Lord and Savior.
Next, lets read the text from a Jewish perspective for the author is giving argument for why Jesus is the capstone of all they held to and trusted in as Jews. They had the prophets but God sent his son, they had Moses who delivered them from Egypt and gave them the Law, but Jesus delivered them from sin, fulfilled the law and delivered a the Law of grace, etc, etc, etc.
Then turn your attention to Hebrews 5:12 where he reveals that his readers are immature and behind in their spiritual growth.
For when for the time ye ought to be teachers, ye have need that one teach you again which be the first principles of the oracles of God; and are become such as have need of milk, and not of strong meat.
Moving on to Hebrews 6:1 he begins to exhort them to move on from what he calls "the principles of the doctrine of Christ." or more literal, "leaving the first sayings (logos) of Christ." But with this exhortation comes a warning starting at verse 4 that if they are not "going on onto perfection" or growing in Christ, then they are in danger of falling away. Now this is where it gets controversial.
The phrase, "For it is impossible," does not mean "never possible," but literally means, "without strength" as in an inability. What is unable for those? "To renew them again unto repentance," if they "fall away," after experiencing the Lord in all the ways mentioned (which is all the ways every believer experiences the Lord when they believe). But "fall away" from what? Well, since they are exhorted to grow in Christ then to fall away is a falling from Christ. Its going the other direction back to what they were. If they fall away after having experienced Christ and after failing to grow and mature in Christ then they are unable or without the strength to (hear comes some more important words) "renew them again onto repentance," or "renew them anew into repentance." Remember that repentance was what led to salvation and simply means "change of mind."
So, "there is no strength or an inability for those. . . if they fall away, to re-new them anew into a change of mind." Why? (The author at this point adds the ????.) Because those who have fallen away "crucify to themselves the Son of God afresh, and put him to an open shame." To understand what the author means by this we simply need to recall why Jesus Christ was crucified in the first place. He was accused of blasphemy, insulting God, by saying he was the Son of God and so claiming equality with God (John 5:17). Therefore, to "crucify to themselves the Son of God afresh," tells us that those he refers to that "fall away" have returned to the same belief that put Christ on the cross in the first place and that they regard him as guilty of blaspheming God and deserves to be crucified and put to an open same.
Now the author is not warning of becoming a carnal believer who has gotten caught up in some kind of sin or false doctrine as did the Corinthians, though this is a real danger as well for Christians not growing, but more directly of those who potentially would return to a denial that Christ is the Son of God and so in themselves and in their mind crucify him. it is a return to disbelief.
So does this answer the question, "Can a believer lose his salvation?" Let me answer with a question. Can a person be called a believer if they don't believe that Jesus is the Son of God? No, so then a believer can not lose their salvation, but for the one who returns to disbelief, well that is a different story. They have not lost their salvation but fell away from it and are turned against Christ.
The real answer is, just keep growing and you have nothing to worry about.