The password cracking attempt described involves the use of Rainbow tables. A Rainbow table is a precomputed table for reversing cryptographic hash functions, primarily for cracking password hashes. These tables store a mapping between the hash of a password and the correct password for that hash, allowing for quick retrieval of the plaintext password if the hash is known. This method is efficient for cracking passwords because it avoids the time-consuming process of computing hashes on the fly during an attack.