IMAP (Internet Message Access Protocol)
IMAP4 allows you to read emails as they appear on the hosting server. Any changes you make (delete, reply, forward, move) are seen by anyone else who logs into webmail or IMAP. This is the perfect solution for multiple users who need to access the same email account. This is also perfect for anyone who needs to access one email account from multiple devices at the same or different times.
POP (Post Office Protocol)
POP3 allows you to download copies of your email messages to your personal computer. Any changes you make will NOT be seen by anyone else who accesses the email account (because you are only making changes to local copies). The copies of the email messages on the server are normally unchanged, but it is very easy to unintentionally setup your POP3 access to delete those server copies whenever you download the emails. This is a perfect solution for a user who has very limited time to be online, but needs to spend lots of time reading emails. This is also a perfect solution for anyone who needs to archive permanent copies of their emails (e.g. before you terminate that email name or its hosting provider).
Most of our clients prefer Webmail due to its ease of use and the fact that it can be accessed with just a web browser. Plus, it also has the same advantages as IMAP. However, webmail depends on a web browser (e.g. Firefox, IE, Opera, Chrome, Safari, etc.) which takes time to load, access the webmail page, login, wait for the GUI to load, browse through a likely limited view of your inbox, and view one email message at a time.
Mail Programs (such as Outlook or Windows Mail or Thunderbird)
A mail program (also known as a "pop client") is required in order to connect via POP or IMAP. A mail program will simply launch from your desktop and gives you rapid access to all your emails (even faster but less secure if you let it remember your passwords). Also, mail programs have advanced tools and features which webmail may not have. There are many to choose from, such as the program included with your Operating System: Microsoft Windows includes either Outlook or Windows Mail, Apple includes Mac Mail. There are also third-party programs such as Mozilla's Thunderbird and Qualcomm's Eudora.