Context is important to know what these words mean. Sergeant major Morris came back from India and told the Whites about a tale of a monkey's paw, which he obtained while he was there. He also stated that the paw was supposed to grant three wishes. But there was a caveat.
A fakir put a spell on it. He wanted people to know that fate ruled the lives of people. In other words, people should not fight fate. According to Morris the last person who used it got two wishes and for his last wish, he wanted death. In light of this, Morris threw the paw into the fire. Here are the words:
Then he took the paw and suddenly threw it on the fire. With an astonished cry Mr White bent down and pulled it out quickly.
‘Better let it burn,’ said the soldier.
'If you don’t want it, give it to me, Morris.'
'No. I threw it on the fire. If you keep it, don’t then say that it is my fault. Be sensible – throw it on the fire again!’
As the story progresses, Morris's beliefs were correct. The Whites use the paw and obtain their wishes in a way that they did not expect. Great tragedy struck. Morris knew that something like this would happen. So, he wanted to destroy it. That is why he threw the paw into the fire and said "let it burn."