What does it mean to blaspheme the Holy Spirit?
First of all the word "blaspheme" means to utter obscenities or profanity, or to speak things that are irreverent and untrue about God.
There are many ways that we can blaspheme, but Jesus spoke of blasphemy against the Holy Spirit in a most serious way. Here is the passage.
Matthew 12:22-32 (NIV)
Then they brought him a demon-possessed man who was blind and mute, and Jesus healed him, so that he could both talk and see. All the people were astonished and said, "Could this be the Son of David?" But when the Pharisees heard this, they said, "It is only by Beelzebub, the prince of demons, that this fellow drives out demons." Jesus knew their thoughts and said to them, "Every kingdom divided against itself will be ruined, and every city or household divided against itself will not stand. If Satan drives out Satan, he is divided against himself. How then can his kingdom stand? And if I drive out demons by Beelzebub, by whom do your people drive them out? So then, they will be your judges. But if I drive out demons by the Spirit of God, then the kingdom of God has come upon you. "Or again, how can anyone enter a strong man's house and carry off his possessions unless he first ties up the strong man? Then he can rob his house. "He who is not with me is against me, and he who does not gather with me scatters. And so I tell you, every sin and blasphemy will be forgiven men, but the blasphemy against the Spirit will not be forgiven. Anyone who speaks a word against the Son of Man will be forgiven, but anyone who speaks against the Holy Spirit will not be forgiven, either in this age or in the age to come.
Jesus said that “blasphemy against the Holy Spirit” was literally speaking a word against the Holy Spirit. Specifically He was referring to the Pharisees who couldn’t deny that Jesus was casting demons out of people, so they manufactured an explanation that Jesus was deceiving the people by casting out demons through the power of Satan. Since Jesus was clearly doing these things through the power of the Holy Spirit, He referred to this as speaking against the Holy Spirit, which He also said was an unforgivable sin. (Click here for a video teaching Pastor Paul did on this subject)