Imagine this scenario:
A person believes, for whatever reason, that eating bananas is sinful. This person's friends (including even a priest) have told him that this is not true. Still, for some unexplained reason, the person continues to believe that eating bananas is sinful. If this person then went ahead and ate a banana, would he be sinning?
I know the example is a bit strange, but it illumines an important point: the "sinfullness" of an action doesn't just depend on the action itself, but also on whether or not we believe (that is, our conscience tell us) that the action is good or bad. If the person above ate a banana, it would be sinful. The reason is that his conscience told him that eating bananas was wrong, yet he did it anyways. In other words he did what he believed was wrong.
Now for ignorance:
A modern day doctor fails to properly diagnose a patient who has AIDs, instead diagnosing the patient with some other condition. This doctor is acting on vincible ignorance and is morally culpable for the state of the patient. In this day and age, there is no reason to miss an AIDs diagnosis.
If a doctor in the 50s were to do the same thing - misdiagnose a patient who had AIDs - he would be acting on invicible ignorance - ignorance that cannot be overcome by himself. There was too little known about AIDs in the 50s for him to make the proper diagnosis. Therefore the doctor is not morally culpable.
These are all reasons that our conscience must be formed properly. It must be formed within the context of the Faith and the Church to properly know what is true and good and what is false and bad.