Final answer:
The cerebellum is the area of the brain that is most important for processing implicit memories, essential for tasks such as motor learning and classical conditioning.
Step-by-step explanation:
The area of the brain most important in the processing of implicit memories, such as procedural memory, motor learning, and classical conditioning, is the cerebellum. Although the hippocampus plays a critical role in processing explicit memories, it is not primarily responsible for implicit memory formation. On the other hand, the amygdala is involved in the emotional aspects of memory and memory consolidation, particularly related to fear and aggression. Therefore, for procedural memories and tasks like classical conditioning, the cerebellum is the key player. For instance, in experiments with rabbits, damage to the cerebellum prevented the learning of a conditioned eye-blink response when presented with a puff of air, highlighting the cerebellum's significant role in this type of implicit memory.