Thomas Putnam is a wealthy land owner in Salem, Massachusetts. He's also the kind of guy or character to hold a grudge. For example, he holds a grudge against Francis Nurse. The reason is that Putnum's brother-in-law was kept from being elected to the office of minister by Francis Nurse.
During Act 3 of the play, Giles Corey accuses Thomas Putnam of making a land grab at the expense of the people being accused and convicted of witchcraft. Giles Corey says that he has a source that says Putnam is prompting his daughter to accuse other land owners of witchcraft. Upon conviction, those people forfeit their land rights, which then leaves the property available for purchase. Putnam is the only Salem resident wealthy enough to buy that much land. Putnam stands to gain a lot of land cheap if his neighbors are convicted of witchcraft.
Giles Corey refuses to give up his source, and is arrested for contempt of court. He is later killed by pressing. He was pressed because he refused to enter a plea. If he had entered a plea, his lands would be forfeit to the government and his family would be left with nothing. So the court decided to "press" a plea out of him. Pressing involves piling stones on top of a prone person's chest until the pain was so great that the person made a plea. It's torture. Every time Giles was asked what his plea was, he responded "More weight." He died after 2 days of pressing.
One more interesting tidbit about Giles Corey is that he supposedly said something like "I curse you [the sheriff] and all of Salem" during the pressing. 4 years later the sheriff died of a heart attack at the age of 30. For the next 300 years, just about every single sheriff of Salem has had to leave office early because of heart or blood trouble, or has died of heart/blood related issues.