From the time somebody is arrested, charged or a warrant is issued, up to the moment when the court finishes dealing with it, the case is said to be sub judice. This is a Latin phrase meaning "under judgment". While a case is sub judice, you are strictly limited as to what you can report.
You may only give details of what is happening officially within the legal process. In practice this means only information which is part of a charge or details which are part of actual court proceedings. You may also mention some details which are not likely to be contested in court.
Several kinds of reports while a case is sub judice may prejudice a fair trial. One has already been mentioned - publishing details of the defendant's previous convictions.
Another is broadcasting details of the background of the case. Whenever there is a big trial, reporters gather together details of the defendant's past life and other background information, ready to publish them at the end of the trial. Once the trial is over, and is no longer sub judice, then all this material can be reported. However, if any of it is published during the trial it may be held to prejudice a fair trial.
If there is no jury, then what is published or broadcast is not so likely to prejudice a fair trial, since the judge will be more able to ignore it. Nevertheless, even in trials without juries there are limits to what will be tolerated and care should be taken not to interfere with the proper course of justice.