POP (Basic)
With POP3, your mail is saved in a mailbox on the remote server until you check your mail. When you check your mail, all of the mail is downloaded to your computer and is no longer maintained on the server. If you use POP3 and are traveling or check your mail from multiple locations, you will not be able to view any of your old mail because the messages only exist on the computer on which you originally received your mail. Note: With POP setup there is an option to keep messages on the server for X days but it will keep everything in inbox only and not have a perfect sync with what you already deleted from your email client.

IMAP (Advanced)
IMAP is a newer protocol that keeps all messages and folders on the server.  Unlike POP, IMAP offers two-way communication between the Mail Server mailbox and your email client(s) mailbox. This means when you log in to the Webmail interface, actions you performed on email clients and mobile devices will automatically appear in the Web interface (and vice versa).  Cons: Since IMAP syncs all messages to Webmail it uses more disk space and if you do not keep old un-needed messages deleted properly it could cause you to have to purchase more disk space.  Also IMAP is considered advanced as it has more settings such as subscribing/syncing folders, marking as deleted and then having to purge, etc.

Need a Free Email Client Program?
A good solid program for Email is Thunderbird, http://www.mozillamessaging.com/
It supports both Windows and MAC.