The difference between outbox and sent is that messages in the outbox are in the process of being sent, but have not yet been sent. If you have a notebook, for instance, and you write an e-mail while you're on an airplane, and have no net connection, then it goes to the outbox, until you get a connection, at which time it goes to Sent. I think you can also set it up so that messages do not get sent automatically, but queue in the outbox until you trigger a send; some people like this because they have a sort of "oh, wait" buffer.
The IMAP server is basically the server that provides incoming mail, and the SMTP one is the one that takes your outgoing mail. If you must enter a password for your SMTP, then what you must do is, in the options for the Outgoing Mail Server, change the pull-down that says Authentication from "None" to the appropriate setting for AOL (probably "Password"). Also, if they require a secure port, change that too. When you change the authentication type, it will let you give the password.
Does that make sense / help?