Deliberate Sin
Heb 10:26 If we deliberately keep on sinning after we have received the knowledge of the truth, no sacrifice for sins is left
Concerning the category of sin he's referring to it is first of all deliberate, intentional, willful. But he's not talking about snapshot events, but rather a chosen lifestyle of deliberate sinning. The NIV is correctly interpreting the usage of the present tense as "keep on sinning", as opposed to if the aorist tense were used which would be referring to point in time events. Furthermore given the "willful" aspect, these are not sins of which one is reluctant to commit due to the weakness of the flesh, nor sins of which one is unaware, being blind spots, but those which one has consciously chooses to define one's lifestyle.
A further condition is not just deliberate sinning, but doing so in light of having received the knowledge of the truth. This is not to say that such people had come to know Christ personally. The word is "epignosis" - mere surface knowledge - to know "about" someone. Granted that one has to know about someone to know him personally. But one can know about someone without having a personal relationship with that person. These are at best nominal Christians, false brothers. For example Peter writes in 2Peter 2:20, "If they have escaped the corruption of the world by knowing our Lord and Savior Jesus Christ and are again entangled in it and overcome, they are worse off at the end than they were at the beginning." Here again "knowing" is actually "epignosis" - knowing about something rather than knowing someone personally.
But in particular it would seem he's talking about the sin of apostasy. Note in verse 28 he makes a comparison with the rejection of the Law of Moses for those Israelites subject to the Law. In this case he is referring to those who had allegedly become "Christians", but later rejected Christ and the gospel of Christ.
We have seen similar things so far in Hebrews in chapters 3, 4 and 6. Note in particular the rhetoric the Heb 6 passage "if they fall away, to be brought back to repentance, because to their loss they are crucifying the Son of God all over again and subjecting him to public disgrace." Heb 6:6 Compare to Heb 10:29 So here he points out that those who essentially leave the faith by opting for a lifestyle of sin also leave behind the sacrifice which could have atoned for their sins. For there is no atonement for those who leave the faith. But let us also remember 1John 2:19 "They went out from us, but they did not really belong to us. For if they had belonged to us, they would have remained with us; but their going showed that none of them belonged to us."