Encryption – More Explicit Explanation for the Retriveal Password Authenticated Key

How can I get an authenticated password? I found a description of PAKR:

A PAKR (Password Authenticated Key Retrieval) protocol and its multi-server system allow a party (for example, the customer) with a memorable password to recover a long-term static key in a exchange of messages with at least one other party. (for example, server) which has a private key associated with the password.

But I can not understand why use "recover" a long-term static key. Does this mean that I can find my private key via trading servers with a password associated with the message? If this is the case, why do we need to store the private key on the server?