fancythat I think 'prejudice' in legal cases like this is to do with influencing potential jury members.
If someone is arrested for, let us say, knocking down and killing a child then in the drivers local area, people may be talking about the driver, exchanging stories about them, saying that they abuse their wife, kick cats, drive recklessly all the time, whether these thing are true or not, and generally bad mouthing them.
Now if the jurors at the trial for the child's death, all came from the drivers local area, they may well go into court with a really negative attitude to th defendant, and be likely to convict the driver even though, once the case is examined, it is clear the child ran out from between two parked cars and the driver could not avoid them.
The prejudice laws aim to make sure that as far as possible those involved in judging a case have not been prejudiced against a defendant in any way before the court case, so if anyone starts sharing information about the person, their past, family history previous convictions etc etc publicly, information that might prejudice the chance of the defendant having a fair trial, they lay themselves open to a criminal charge.