A trial is either by jury or a bench-trial (meaning by judge only).
Juries have a way of letting emotion and circumstance influence their decision, whereas a judge might be much less inclined to focus on anything other than the correct legal result. For instance, if a defendant is on trial for murder, but claims that the act of killing was done in self-defense, the defendant may want to appeal to the jury members' emotions. Sometimes the evidence (witnesses, police reports, etc.) may not completely support the defendant's case, but a sympathetic jury might still come back with a verdict of not-guilty.
On the other hand, if the jury is not likely to sympathize with the defendant, but the evidence is strong in the defendant's favor, the defendant may prefer a bench trial. Perhaps there is strong evidence that the defendant did not commit this crime, but the defendant has a previous criminal record which could hurt his/her chances of success with a jury who does not like criminals.
Whether to seek a trial by jury is ordinarily going to depend on the specific facts of the case-at-hand.