If it's a POP account:
Settings>Mail, Contacts, Calendars>your AOL account>Advanced>Delete From Server. You will have three choices, Never, Seven Days, When removed from inbox.
If it's an IMAP account, open the settings for that account, and look down at the bottom of the first page, and see if you have a selection for "archive messages". I have Gmail set up as IMAP and it has that setting.
I believe that I have read that you can set it up as POP, but I don't know what the server settings are.
AOL uses IMAP so it won't erase your emails from the server after you download them, if you read them on your iPhone then they will appear on your old mail folder when you check it on your computer. If you delete them on your iPhone then they will be deleted from the server.