IMAP allows all mail (including your Sent, Drafts, Spam and Trash folders, as well as custom folders) to live on the server. This is one of the main benefits of IMAP, since your account is identical whether accessing your mail from any workstation or webmail. The problem is that hosts create different sets of default folders when you create a new account, and that Mail.app doesn’t automatically connect the folders on the server to its local functions (most importantly, Sent mail and Drafts).
Dan Rubin at Superfluosbanter.org explains how to set up Mail.app. Click here for his explanation.
On our servers, the inbox is called INBOX, in capitals.