I am assuming that the second password is like decryption key.
I have saved the second password as "mailbox password"
The way I interpreted is that first password is for the account, so verify I am who I say I am.
But since the emails are encrypted, browser can't show my messages in human-readable form.
Second/mailbox password decrypts it and shows the emails in human readable format.
This is just a guess.
I would love to hear about second password from other/more knowlegeable folks.