Fundamentally, blasphemy means dishonouring or insulting God by words or actions. Under the Law of Moses the punishment was death by stoning. Leviticus 24:15-16 says, “Whoever curses his God shall bear his sin. Whoever blasphemes the name of the LORD shall surely be put to death. All the congregation shall stone him.” For example, in 1 Kings 21:8-16 Jezebel arranged for Naboth to be falsely accused of blasphemy and he was stoned to death. The charge was that he had cursed God and the king.
When Jesus healed a blind and dumb man the Pharisees attributed his power to Beelzebub, the prince of demons (Matthew 12:24). Jesus accused them of blaspheming against the Holy Spirit because they did not give God the glory. He says, “Every sin and blasphemy will be forgiven people, but the blasphemy against the Spirit will not be forgiven.”
So, to blaspheme means to dishonour God.