When you are on course, there is a particular path, trail, route, road or prescribed direction which you are expected to take. If you deviate, then you are off course. You could have finished the race like the rest of the contestants except you ran off course.

If you are "off course", you have left the defined or normal path. A marathon runner who by accident leaves the designated route of the race has "run off course". The expression can also be used figuratively for example for businesses, or politicians. e.g. The election candidate's latest controversial remarks show that he has really run off course in this campaign.