When you receive mail in the Physics department, it first arrives in the system mailbox. This is a simple file in the system directory /var/spool/mail. The name of the file is the same as your login name and you are the owner of that file. The system mailbox should be considered a temporary place for your mail. It is not appropriate to let mail pile up there, since it is a shared resource with finite space.
From Physics department computers there are various utilities for reading your mail with various methods for handling the mail from there. The most popular utilities such as thunderbird and pine remove mail from the system mailbox and put it in a ``folder'' called ``Inbox''. You can move messages from there to other folders. Those folders are simple files created in your home directory under subdirectories that the mail utility creates for itself. Since each utility is likely to have its own directory, it is best to stick with one utility for moving mail so you don't lose track of your mail folders.
There are also web-based mail utilities. The Physics department web-mail utility is accessed through the URL http://mail.physics.utah.edu. Its Inbox is the system mailbox itself, and it does not move mail automatically from there to another folder. This type of operation is called ``IMAP'' for Internet Message Access Protocol.
From your home computer or, for that matter, from any computer that is not part of the departmental Unix system, you can configure your local mail utility so it moves mail from the Physics department mailbox to your local computer. This sort of configuration is called ``POP'' for Post Office Protocol. It actually transfers the mail files. Obviously, you need to decide where you want to keep your mail before setting up such an operation.
When you send mail through the Physics department, your message is transferred to the departmental mail server and sent from there. Since this sort of mail reflection has been commonly used to launder SPAM, most mail handlers now require user authentication before agreeing to process mail from outside computers. This is true of most internet sevice providers as well as the Physics department.