Therefore let us leave the elementary doctrine of Christ and go on to maturity, not laying again a foundation of repentance from dead works and of faith toward God, and of instruction about washings, the laying on of hands, the resurrection of the dead, and eternal judgment. And this we will do if God permits. For it is impossible, in the case of those who have once been enlightened, who have tasted the heavenly gift, and have shared in the Holy Spirit, and have tasted the goodness of the word of God and the powers of the age to come, and then have fallen away, to restore them again to repentance, since they are crucifying once again the Son of God to their own harm and holding him up to contempt. For land that has drunk the rain that often falls on it, and produces a crop useful to those for whose sake it is cultivated, receives a blessing from God. But if it bears thorns and thistles, it is worthless and near to being cursed, and its end is to be burned. (Hebrews 6:1-8)
The writer of Hebrews continues his thoughts regarding maturity in Heb 5:12-14. The Gospel is very simple but there comes a time when believers need to move past just the rudimentary and into the deeper. Not every Christians is called to be a professional theologian, in fact I am not sure any of us are called to that, but we are called and expected to move past a basic knowledge and into the weightier questions. The New Testament speaks a lot about the Gospel and what we must do to be saved but it also speaks quite a bit about what we are to do once we have been saved.That is where these sorts of issues come into play about moving past the elementary.
The second portion of these verses is where it gets more muddled and much harder to interpret. It certainly sounds at first blush as though true regenerate believers can fall away, and not just fall away but fall away in such a sense that they are never able to be redeemed. This is a tough one. The rest of the New Testament seems to paint a picture of what is commonly caled "eternal security" but what to do with this? The first bit of advice here is to appraoch this slowly and with a great deal of caution.
This is also a case where the correct hermeneutic is to interpret difficult, less clear passages through the lens of more clear and direct passages. Looking at some other verses might help to clarify this passage. First, the Bible makes mention of those who outwardly profess the faith but end up being shown to be false later....
They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us. (1 John 2:19)
Were these who went out actual believers? I don't think so. They were "with us" but then the went out because they were "not of us". I think most of us know either personally or from anecdotal evidence of someone who seemed very religious and then went off the rails. In a religious culture it can be pretty easy for someone to skate along for a long time without ever being born again. I personally get concerned when someone tells me that they have "always been a Christian". The reality is that we cannot know for sure that anyone is regenerate and those who leave serve as a reminder of this fact.
As I read this my mind also went to the parable of the sower that Christ taught....
And he told them many things in parables, saying: "A sower went out to sow. And as he sowed, some seeds fell along the path, and the birds came and devoured them. Other seeds fell on rocky ground, where they did not have much soil, and immediately they sprang up, since they had no depth of soil, but when the sun rose they were scorched. And since they had no root, they withered away. Other seeds fell among thorns, and the thorns grew up and choked them. Other seeds fell on good soil and produced grain, some a hundredfold, some sixty, some thirty. He who has ears, let him hear." (Matt 13:3-9)
The sowing here is of the Gospel, even on infertile ground (i.e. unregenerate hearts) there can be some signs of life but ultimately the lak of fertile ground becomes apparent. But seed that falls into good soil sprigns up. We don't kknow which soil is good versus not so we sumply proclaim the Good News to all men everywhere and trust in He who is faithful to move men to repentance.
That is a pretty unsatisfactory answer to a question that has caused controversy for a long time but that is all I got at this point!