Moisture and tars accumulate near the head of a cigar as you puff. At some moment during the smoke, typically when there is about a third or less of the cigar remaining, the flavor of the cigar can change, and get bitter, or somewhat harsh. That moment is referred to when a cigar ‘turns.' The oils and moisture have accumulated and have tainted the flavor of the cigar.
There is no set rule for when a cigar does or does not turn. We have smoked cigars that didn't turn at all, and have very carefully smoked cigars down to the point where very little cigar remains. Some of us have put our facial hair in danger of flame while doing this.
If you opt to smoke a cigar down to the very end, be careful and remember the end of the cigar is lit.