Well, that all depends on many different things.
If the Outlook client is configured so that it knows that the Exchange server <b>is</b> an exchange server, then all communication takes place over MSRPC (MicroSoft Remote Procedure Call), which also requires that several other remote services be running on the server and client machines.
If the Exchange server is meant to communicate with other email clients (the default), then the Outlook configuration has the option of using IMAP or POP3 as a mail retrieval, and SMTP for sending mail.
IMAP allows the mailbox(es) to remain on the server, and the Inbox view is essentially just that; a view into the inbox or other folder.
POP3 is an older protocol (from Unix days) where the client logs into the remote server and copies down the emails to the local machine.
The typical scenario is for Exchange to communicate with Outlook using MAPI.
However, with Exchange 2000 and 2003 you also have other options including allowing POP, IMAP, and RPC over HTTP or HTTPS. I haven't worked with the newer servers, but I suspect they're the same in those respects.
Finally, you can use Outlook Web Access to access your emails using any web browser.
You didn't ask, but it's worth mentioning that the Macintosh Email client from Microsoft called Entourage is actually a webmail client - despite its close resemblance to Outlook
Did you need more specific information?