The phrasal verb 'put through' can mean to connect somebody by telephone. So, you can 'put a call through' or ask to be 'put through' to someone in order to speak to them. To be 'put through something' can also mean to experience something difficult or unpleasant, usually as a test or an unpleasant ordeal. You can also use 'put through' when you want to talk about something that you have followed through to its successful conclusion. So, you can 'put a deal through'; a proposal could be 'put through'; or you can 'put someone through college' or school. This last example can also refer to paying for someone to go to college.
Additional examples with 'put through' are:
In a job description, it indicates that training is offered:
"All applicants will be put through training before placement."
At the hospital, the doctors are unable to make a diagnosis:
"We will need to put you through a few tests before we can determine what is wrong with you."
In Customer Service, you encounter a customer who is unhappy:
"I have a customer on the line who asked to be put through to the Manager."