One good example is to avoid blame, or at least to lessen the obviousness of it. For examples, someone might say, "Mistakes were made" instead of "I made a mistake."
Also, the passive voice could be used to take the focus off the subject and onto what is more important.
Example: "Every student was given a chance to improve his or her grade." That's passive. Active would be "The teacher gave every student a chance to improve his or her grade." The point is that every student got a chance. Using the active voice with "the teacher" puts the focus back on the teacher and how great it is that he or she gave the students a chance, when what we really want to focus on is that they got the chance, regardless of who gave it to them.
Did I explain that okay?