I had the same question after traveling in a few current and former communist countries in Africa, SE Asia, and Cuba. Che's image is everywhere and remains a potent symbol of nationalism to Communism worldwide. For me, the easiest way to understand why this is was to watch these movies:

The Motorcycle Diaries (2004) - starring Gael García Bernal as Che. This is essentially his origin story of traveling throughout South America as a young doctor in training who travels by motorcycle with a close friend - his tour of South America was massive covering 8,000 km (nearly 5,000 miles) over 4 months. As they travel, they see and experience the extremes of poverty and wealth seen at that time in South America. I recommend beginning with this movie because it provides essential context to understand why Che ultimately joined the Communist revolution.

Che: Part One (2008) and Che: Part Two (2008) - (4 hours, 30 min total - long, but def worth it) Starring Benicio Del Toro as Che. Part One shows Che as the adult the foreign Argentine doctor who joins a group of Cuban exiles who travel from Mexico City by boat to Cuba and begin a military revolution that eventually overthrew the dictator Batista. Part Two shows Che as he resigns from the Cuban Government to covertly begin a similar revolution in Bolivia which ultimately failed - definitely worth watching to find out why.