The book of Hebrews was written to saved people. They happened to be Hebrews (Jews), but they were already saved people nonetheless. (See section 17)
HEBREWS 3:1 Wherefore, holy brethren, partakers of the heavenly calling, consider the Apostle and High Priest of our profession, Christ Jesus;
and
HEBREWS 4:1 Let us therefore fear, lest, a promise being left us of entering into his rest, any of you should seem to come short of it.
HEBREWS 4:2 For unto us was the gospel preached, as well as unto them: but the word preached did not profit them, not being mixed with faith in them that heard it.
HEBREWS 4:3 For we which have believed do enter into rest, as he said, As I have sworn in my wrath, if they shall enter into my rest: although the works were finished from the foundation of the world.
and so on...
The letter to the Hebrews, therefore, does not tell anyone how to become saved (because they were already saved by the time that it was written). Although the book of Hebrews never really discusses how an individual becomes saved, the sacrifice of Jesus Christ on the cross, and what that implies, is discussed. (In Hebrews, such things are written in a very oblique, allegorical way, and is therefore more difficult to follow than the rest of the New Testament.)
In Hebrews 5:11-14, the writer, presumably Paul, began to rebuke the Hebrew readers as those who didn't understand the scriptures as well as they should. It is in this context that the writer continued:
HEBREWS 6:1 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,
HEBREWS 6:2 Of the doctrine of baptisms, and of laying on of hands, and of resurrection of the dead, and of eternal judgment.
HEBREWS 6:3 And this will we do, if God permit.
When the writer wrote of "leaving the principles of the doctrine of Christ" in verse one, he did not mean "forsaking the...doctrine of Christ." Instead, he only meant this conversationally, meaning that he would not write about the basics of the doctrine of Christ at this time, but that he was going to write as though they did understand ("let us go unto perfection"), not re-explaining the basics yet again ("not laying again the foundation..."). Next, the writer wrote his reason for this decision, saying:
HEBREWS 6:4 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,
HEBREWS 6:5 And have tasted the good word of God, and the powers of the world to come,
HEBREWS 6:6 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.
By the time this was written, the Son of God had already risen from the dead, and had ascended into heaven. It is obviously not possible to literally crucify Him again, therefore the meaning of this clause must be symbolic, rather than literal. Referring back to section 18, recall what Paul wrote:
ROMANS 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
ROMANS 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
ROMANS 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
ROMANS 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
(See section 18 for more on this scripture). According to Romans 6:3-4, it is by baptism (water baptism) that we are baptized into Christ's death. Christ Himself died by crucifixion. Therefore, it is by baptism that one "crucifies to himself the Son of God" (Hebrews 6:6).
HEBREWS 6:4 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,
HEBREWS 6:5 And have tasted the good word of God, and the powers of the world to come,
HEBREWS 6:6 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.
To "crucify to themselves the Son of God afresh" means to be baptized (in water), in the name of Jesus Christ a second time. According to Hebrews 6:4,6, this is not permissible.
In like manner, Hebrews 6:6 infers that to "crucify the Son of God to [one]self" (i.e., baptism) is for renewal unto repentance. Romans 6:4-6 makes the identical point:
ROMANS 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
ROMANS 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
ROMANS 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
ROMANS 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
It is by baptism that we are buried with him into his death (verses 4-5), "that the body of sin [is] destroyed" (verse 6), and that therefore, we should walk in "newness of life" (verse 4). This describes a "renewal unto repentance" perfectly:
HEBREWS 6:6 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.
Therefore, the word "renew" from the phrase "to renew them...unto repentance" refers to a water baptism. "Unto repentance" refers simply to repentance. If you will recall, we were commanded both to repent, and to be baptized:
ACTS 2:38 Then Peter said unto them, 1) Repent, and 2) be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Keeping all of this in mind, Paul wrote:
HEBREWS 6:4 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,
HEBREWS 6:5 And have tasted the good word of God, and the powers of the world to come,
HEBREWS 6:6 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.
This means (in part) that a believer may not be re–baptized: it would put Christ to an open shame (Hebrews 6:6). After all, Jesus said:
JOHN 3:3 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.
He was only talking about one birth. (He did not say, Except a man be born again, and again, and again... (See section 3).
Let us take the time to briefly re-visit section 16:
ACTS 19:1 And it came to pass, that, while Apollos was at Corinth, Paul having passed through the upper coasts came to Ephesus: and finding certain disciples,
ACTS 19:2 He said unto them, Have ye received the Holy Ghost since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
ACTS 19:3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
ACTS 19:4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
ACTS 19:5 When they heard this, they were baptized in the name of the Lord Jesus.
ACTS 19:6 And when Paul had laid his hands upon them, the Holy Ghost came on them; and they spake with tongues, and prophesied.
These men had previously been baptized with the baptism of John. Although John's baptism has since been superseded by water baptism in the name of Jesus Christ, and is therefore no longer valid, it was at one time ordained by God. Nevertheless, when these disciples heard the word of the Lord, they were re–baptized "in the name of the Lord Jesus."
These men were born of water and of the spirit (John 3:5) only once. That was done when they were "baptized in the name of the Lord Jesus," at Acts 19:5.
Today, there are many, many heretical baptisms, which are patterned after the traditions of men, and not patterned after Christ. Some don't baptize at all. Some sprinkle or pour, but do not immerse in water. Most are baptized with the words "in the name of the Father, and of the Son, and of the Holy Ghost," perhaps never realizing that the name of the Father and of the Son and of the Holy Ghost is Jesus Christ. Those who are baptized in this way, (like the previous baptism of the disciples of Acts 19:1-6) are typically baptized in ignorance, and not malice.
If you have not been baptized in water (immersed in water) in the name of Jesus Christ (where the baptizer actually says something like "in the name of Jesus Christ"), then why not do as the disciples of Acts 19 did? They will be saved, and will have eternal life—so why not you?
It really is a matter of eternal life, or of eternal death.