Here is my 2 cents worth:
The concept of blaspheming the Holy Spirit comes from Matthew (12:31-32), Mark (3:28-30), and Luke (12:10). Here is the passage from Matthew:
"Therefore I tell you, every sin and blasphemy will be forgiven people, but the blasphemy against the Spirit will not be forgiven. And whoever speaks a word against the Son of Man will be forgiven, but whoever speaks against the Holy Spirit will not be forgiven, either in this age or the age to come."
This passage has been the subject of much debate and interpretation within Christian theology. My consensus is that to blaspheme the Holy Spirit is to consciously, persistently, and deliberately reject the work and witness of the Holy Spirit. It's seen as a hardened state of willful unbelief.
The specific context in the gospels is that Jesus was performing miracles, and the religious leaders of the time were attributing His power to do these things to Beelzebub (a demonic entity) rather than to the Spirit of God. This attribution of God's work to an evil source is seen as blaspheming the Holy Spirit.