POP3 is the most common type of mailbox.
It acts as a post office, when you pick up the mail it disappears from the post office and you now have the email on your device.
However, you can set up your email program to tell the server to store a copy on the server. The advantage of POP3 is you can always see your mails without internet access because it is stored on the device.
Is a more advanced mailbox that provides the ability to synchronize your mailbox between your devices.
IMAPs work by keeping track of all your emails, and you read them directly on the server. Unfortunately, that means it often requires an internet access to read its mail.
The advantage of IMAP is that you can easily keep track of all your mail between several devices such as computer, mobile, tablet, etc.
Is the most advanced type of mailbox. It works a bit like IMAP, all your mail is on one server.
The advantage of Hosted Exchange is the ability to share one's Calendar, Mailbox and Mobile Sync.