sbm12's explanation is right on. Using a POP account and not deleting email as you read them allows the Inbox to get large which increases the chance that the PC will lose track of what it has already downloaded and just download them all again. Outlook doesn't have a duplicate email removal tool, but there are a number of tools available for purchase.

The free workarounds mentioned above will work. As mentioned, you really ought to switch to IMAP if you want to read email on multiple PCs.