What is the 'unpardonable sin'?
The unpardonable sin is defined as blasphemy of the Holy Spirit. This sin occurred when Jesus was talking with the Pharisees. He had performed many miracles and was speaking to the people through the power of the Holy Spirit. However the Pharisees said He was not speaking through or doing these miraculous things through the Holy Spirit but through a demon. Essentially they were taking the Glory of What Jesus was doing and gave the credit to Satan.
"Now when the Pharisees heard it, they said, "This fellow does not cast out demons, except by Beelzebub, the ruler of the Demons." Mat. 12:24
This is blasphemy of the Holy Spirit which was the unpardonable sin at that time. Another scripture that speaks of this is;
"Every sin and blasphemy will be for given men, but the blasphemy against the Holy Spirit will not be forgiven men. Anyone who speaks a word against the Son of Man, it will be forgiven him; but whoever speaks against the Holy Spirit, it will not be forgiven him, either in this age , or the age to come." Mat. 12:31-32
It was this not believing in Jesus, that He was speaking and performing these miracles through the Holy Spirit and saying it was a demon that was Blasphemous.