Data recovery is usually required in one of two cases:
Data was stored in a persistent mechanism such as a magnetic medium or flash memory, and that storage media has become damaged so that it cannot be read normally.
Data was stored in an obfuscated state, such as having been encrypted, and the key or credentials needed to recover the data have been lost.
In IT Security, questions asked are usually concerned with the second reason; recovery of data from an encrypted or hashed state (questions relating to recovery of data from damaged storage are usually asked on the Super User or Server Fault SE sites). This goal is usually frustrated by the very purpose of such methods; to make it infeasibly difficult to obtain the "plaintext" from the "ciphertext" or "hash".
Some common data encryption systems, especially those used to protect user accounts, have some sort of recovery option built in. This "back door" is designed to allow an administrator an alternate way to retrieve the data using their own credentials or other high-level secrets. However, many systems that place a primary emphasis on account or data security, provide only one efficient way to retrieve the data; know the password. Without a "back door", administrators or other "white hats" attempting to get the data for innocent purposes are limited to using the same "attacks" that someone with nefarious goals would have: "brute-force" cracking, or any documented attacks on the specific encryption scheme used by the system.