What makes the Cache API in Drupal 8 any better than Drupal 7's cache system? What's so revolutionary about it? Which of the old limitations does it remove? What are those new concepts and terminology that you should learn about?

And, most of all: how complex is it to set up a cache in Drupal 8 for a specific use case?

You might have already bumped into terms like “max-age”, "context cache" or "cache tags".