The owner of the RSA key can't store the key, so they need to hand the key to an untrusted entity for storage. Before they hand it over they encrypt it using AES with a multi-word phrase they can remember.
The idea is that I could generate a private key and store it outside the entity in a non-secure location but not worry (as much) about it since it is protected by a passphrase.
The private key might be stored in several places - in fact and I have to assume they are all publicly-accessible (like a web page). But when the entity wants to do something with the key it requests it back from the storage places and then (with the users password) decrypts it and uses it for what is needed.