Password Based Encryption (PBE) is specified in e.g. RFC 2898 which specifies the "PKCS #5: Password-Based Cryptography Specification
Keys used for symmetric ciphers such as AES and Twofish should be fully randomized. Passwords, even strong ones, do not consist of randomized bits. So they need to be converted to keys before symmetric encryption can take place.
Furthermore, the passwords do often not contain enough entropy to be used as key, even after - for instance - hashing them with a cryptographically secure hash such as one of the SHA hashes.
Finally, it would be easy to pre-calculate keys that were just hashed with a cryptographically secure hash (rainbow tables). It could also be possible to find which ciphertext was created with identical passwords, although this depends on the protocol.
For this reason a Password Based Key Derivation Function or PBKDF is deployed. PBKDF2 is used in the latest specs. bcrypt and scrypt may also used in other protocols. Sometimes this function is also known as a password hash. Such a PBKDF function also requires a salt (per encryption, stored with the ciphertext) and a work factor or iteration count.
The salt is used to make sure that identical passwords do not calculate to the same key. Furthermore, the salt makes it impossible to use rainbow tables and much harder to perform dictionary attacks.
In principle the same mechanisms can be used afterwards as symmetric encryption with a key. It is however also possible that the symmetric key is used to decrypt a private key such as a PGP key. This key can then be used to decrypt ciphertext that was encrypted using the public key of the key pair.