A ransom is the money that has to be paid to someone so that they will set free a person they have kidnapped.

If you ransom someone who has been kidnapped, you pay the money to set them free.

If a kidnapper is holding someone to ransom or holding them ransom in British English, or is holding a person for ransom in American English, they keep that person prisoner until they are given what they want.

If you say that someone is holding you to ransom in British English, or holding you for ransom in American English, you mean that they are using their power to try to force you to do something which you do not want to do.

If you refer to a sum of money as a king's ransom, you are emphasizing that it is very large.