The waves got higher and higher.

Then the waves broke the boat, and the emperor could not get back to the palace.

(What is the meanign of 'Then' in the passage above? 1. At that time 2. After that 3. In that case Or another meaning?)

In that sentence, it means "after that" -- the next thing that happened.

In the passage provided, the word "then" is used to indicate the sequence of events. It suggests that the waves getting higher and higher was followed by the breaking of the boat, which ultimately prevented the emperor from returning to the palace. Therefore, "then" in this context denotes "after that" and indicates a chronological order of events. So, option 2, "After that," is the meaning of "then" in this passage.