The idiom 'to put the screws on to somebody' comes from the torture device of thumbscrews. When you 'put the screws on someone' it means to put pressure on someone or use the threat of force to coerce someone into doing what do you want.

1. The criminal put the screws on the witness to make sure he didn't talk to the police.
2. My family put the screws on me to spend the holidays with them. 

1. If the supplier sends us another late shipment, our lawyers will put the screws to them.
2. Brian's coffee shop is struggling, and now his creditors are putting the screws on him.