Final answer:
The hernia described, with ischemic contents and inability to reduce, is best classified as a strangulated hernia, which requires emergency medical intervention.
Step-by-step explanation:
The best description of the hernia in question, where the contents appear ischemic and cannot be pushed back into the inguinal canal, is strangulated. A strangulated hernia is a serious condition where the blood supply to the herniated tissue is cut off, leading to tissue death if not treated urgently. The presence of pain and the inability to reduce the hernia back into the canal are indicative of strangulation, which differs from reducible, recurrent, or incarcerated hernias, although incarceration often precedes strangulation.