Without an impartial judiciary, a trial is meaningless. Even when there is a jury present, it is the function of the judge to make sure each side's rights are preserved, and a judge who is not impartial is unable to do this. Furthermore, there are many trials in which there is no jury, and then it is even more important to have an impartial judge.
Judges have great power in the proceedings before them, even when it is the jury that comes to a decision. By definition, a judge who is not impartial is a judge who is going to favor one side or the other. It is the judge who rules what evidence will or not come in. A judge who is not impartial may exclude evidence that is exculpatory, at the expense of the defendant. A judge who shows partiality may allow in hearsay evidence that a jury should not hear. A judge can decide whether or not a hearing is televised, which may favor one side or the other. The judge decides whether or not there is to be a change of venue. When there is a prejudice against the defendant in a particular venue and the judge is biased against the defendant, the judge may rule against a change of venue, knowing full well it will hurt the defendant's case. Alternatively, a judge might dislike a prosecuting attorney and through various rulings, allow defendants to go free. In civil proceedings, there are judges who favor certain kinds of plaintiffs or defendants, as well, and they can influence the outcome in similar ways, excluding or allowing evidence, giving one side greater latitude in cross-examination, or allowing or not allowing an expert witness to testify.
While we all have the right to a jury for criminal proceedings, there are many instances in which defendants do not exercise this right and it is the judge who makes the decision. In some civil matters, there is not a right to a jury trial at all, so in those cases, the judge makes the decision and has all the same means of sabotaging a fair trial. If he or she is not impartial, the results reflect this, a ruling for the plaintiff, for example, where the judge is biased against a particular group of people, or a judgement for the defendant where the judge has a bias for a particular group of people.
There is a procedure whereby a judge can state that he or she cannot be impartial and recuse him or herself from the proceedings. But this is rarely done, even when judges have received campaign contributions from a defendant or plaintiff. This causes the issue of judicial impartiality to continue to be important in our system. If we cannot count on our judges to be impartial, the right to a trial can be worthless.