What is Exchange?
Microsoft Exchange offers email, contacts, shared calendars and other functionality. On the Windows side Outlook is the application for Exchange. On the Mac side Entourage/Outlook and Mail can access Exchange servers. AppleMail only supports Exchange mail. Exchange comes in different flavors - in Microsoft style in year versions. There are currently versions 2007, 2010 and 2013. Under the hood Exchange can use POP, IMAP, and SMTP. In 10.5 Leopard Mail could talk to Exchange servers only via IMAP and SMTP. Snow Leopard added native support to talk to an Exchange server directly. Lion added support for Exchange 2010. Version 2013 is quite new.
Benefits of Exchange
Exchange is supposed to be a robust implementation of email protocols for businesses of all sizes. There is no reason to use this in a private environment. For an Exchange user the handling is almost like with IMAP. Like IMAP the mails are stored on the server and any local change is reflected back to the server.
Drawbacks of Exchange
Exchange accounts can only be accessed by Mail and Entourage/Outlook on the desktop. iPad and iPhone can access Exchange accounts, too, but don't have push notifications. This means that you need to wait for the next scheduled download of the mails or you need to do get mails manually.