(the police) hold (someone) without a trial

When the police "hold" a person, they keep them in jail.

If a person has been convicted of a crime and sent to prison, you don't use the word "hold". You use "hold" for a temporary stay in a jail. Usually a person is "held" by the police for a day or a few weeks:

We're going to hold him here overnight.

He's being held in the Vance County jail on suspicion of drug trafficking.

However, in some countries, the police can "hold" a suspect "without a trial" for a lot longer. This means that the police don't have to prove that you committed a crime. They have the power to hold people in jail for as long as they want.

(do something) indefinitely

Doing something "indefinitely" means doing it without an end point.

For example, imagine that a police officer gets suspended from her job because she did something wrong:

A: How long is she suspended for?

B: Indefinitely.

This means that a time hasn't been set for her to return to her job. She might be allowed to return in a few weeks, or she might never be allowed to return.

The word "indefinitely" is a little technical-sounding, so people use it for talking about serious topics.