Hash-based sharding in MongoDB works by taking the shard key from a document, applying a hash function to convert it into a numeric hash value, then using modulo division by the number of shards to decide which shard stores the document. This method helps distribute data evenly across shards. The execution steps show extracting the shard key 'user_id' with value 12345, hashing it to 67890, then modulo 3 gives 0, so the document is stored in Shard 0. Variables like shardKey, doc, hashValue, and shardNumber change step by step as the document moves through the process. Key points include why hashing is used for distribution, how modulo picks the shard, and that different keys can map to the same shard. The quiz questions check understanding of hash values, step order, and effects of changing shard count.