The Holy Spirit is a member of the Godhead, of equal importance as the father and son.
Now, Jesus freed us from the bondage of sin by dying on the cross. After freeing us he returned to heaven and transfered the authority he gained on earth to us. (the authority we originally had in the garden)
This authority, and the process of becoming completely free from sin, is administerd to us by the Holy Spirit who is on earth with us now.
To blaspheme against the Holy Spirit, is to deny and hold everything Christ did for us in contempt. The Holy Spirit is what Christ gave us, its why he died, so that we could be free. To Mock the Spirit, is to mock Christ's work and the salvation he provided which in a way is a self condemnation.
If you were to die to give someone a precious gift, I think its justifiable to not forgive those who mock it.
(In my head, that's basically why its bad)
Mechanically, blasphemy against the Holy Spirit would be holding Him and his Gifts in contempt, openly speaking against Him or the things of the Holy Spirit, attributing traits to Him that are not of Him (like anything evil for example) etc.
The Holy Spirit is a big deal, we have a duty to get to know our comforter who Christ sent us, and we should respect him as any member of the Trinity.