That's a great question and one that has sparked a lot of theological debate over the years. It's a tough one because the passages that mention it (Matt. 12:32, Mark 3:29-30, Luke 12:10) don't clearly elaborate what "blasphemy against the Holy Spirit" is exactly. Despite this, we can still figure some of it out. When you run into a tough teaching of Jesus, a great first step is to look in the story to see what prompted Jesus' teaching. In the case of Matthew 12, it was the Pharisees saying the Jesus is performing miracles (driving out demons) by the power of Beelzebub or Satan (v. 24). So, it's a good bet to say that this accusation is somehow related to blasphemy against the Holy Spirit. Also, the phrase "So I tell you" is a conjunction connecting this statement, with the previous thoughts in vv. 25-30.
Let's start with the term blasphemy. It typically means to speak against someone, to slander them, to insult or degrade them, or to say harmful and untrue things about them. So, in this story, what's the slanderous insult that the Pharisee's are saying against the Holy Spirit? I think the secret is in v.28 when Jesus says that he drives out demons by the "Spirit of God" (think Holy Spirit).
Putting these together, we can understand "blasphemy against the Holy Spirit" to be the hateful slandering of the work of the Holy Spirit through Jesus by attributing it to Satan. This is much more than just rejection of Jesus, it involves 3 things:
- Knowledge of who Christ is and the power of the Holy Spirit working through him. (The Pharisees had just seen Jesus heal a demon-possessed man.)
- A willful rejection of these facts (who Christ is and how the Holy Spirit works through him).
- Attributing of the work of the Holy Spirit in Christ to the power of Satan.
In such a case, the Pharisees (or even people today) had developed such a hardness of heart that they would have already rejected any ordinary means of forgiveness. In essence, they have cut themselves off from repentance and saving faith in Jesus Christ. This sin will not be forgiven because the person refuses to ask forgiveness not because God doesn't offer it.
I think sometimes we fear that we've committed a sin that God cannot or will not forgive, and that there is no hope for us. But the truth is we only need to come before God, humbly confess that sin (admit it), repent of it (turn away from it), and accept God's promise of forgiveness. God is ready to forgive any sin if we come to him -- 1 John 1:9 promises it: "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness."
Returning to the topic of "blasphemy against the Holy Spirit", I'll quote a famous theologian (Louis Berkhof):
We may be reasonably sure that those who fear that they have committed it and worry about this, and desire the prayers of others for them, have not committed it.