It depends on if you are connected to an exchange server. If this is your
company's computer and they use Exchange, most likely your email is kept on
the exchange server. However, this is a setting that if not locked can be
changed. The easiest way to identify this is take a look at the folder list.
Are all your emails and "boxes" under the heading of Persoanl Folders or
Mailbox-"username"?
If it is Personal Folders, then they are most likely stored locally on your
computer.
If you right click on Personal Folders and then left click on Properties.
Click on the Advanced button and the location of your (.pst) personal folder
will be listed in the box next to Filename: