The same story found in Matthew 12 is echoed in Mark's gospel in chapter 3. Except in Mark's account we see Jesus actually clarify what blasphemy against the spirit was.
22 And the scribes who came down from Jerusalem were saying, “He is
possessed by Beelzebul,” and “by the prince of demons he casts out the
demons.” 23 And he called them to him and said to them in parables,
“How can Satan cast out Satan? 24 If a kingdom is divided against
itself, that kingdom cannot stand. 25 And if a house is divided
against itself, that house will not be able to stand. 26 And if Satan
has risen up against himself and is divided, he cannot stand, but is
coming to an end. 27 But no one can enter a strong man’s house and
plunder his goods, unless he first binds the strong man. Then indeed
he may plunder his house. 28 “Truly, I say to you, all sins will be
forgiven the children of man, and whatever blasphemies they utter, 29
but whoever blasphemes against the Holy Spirit never has forgiveness, but is guilty of an eternal sin”— 30 for they were
saying, “He has an unclean spirit.” -Mark 3:22-30
So to answer blasphemy is in general to be defiant towards or to deny God. Which man by nature is pretty much 24/7 which is why this can be forgiven. Blasphemy against the Holy Spirit is to deny the Holy Spirit. The best example would be by being unsaved, i.e. not believing in the Holy Spirit and therefore not being filled with the Holy Spirit and being saved. Which is as it were the only thing that is unforgiven. Unbelief.
At least that's my take on it.
Hope this helps, God bless.