Simplified explanations of these so I can reference the acronyms
Simple Message Transfer Protocol. Allows you to send a message to your email (providers) server, which then routes it to wherever it has to go, and then stores it on their providers server, till the other person email client grabs that.
Well, how do clients grab email?
Internet Message Access Protocol
Synchronizes from one or more devices. Allows you to read mail on one client, and it gets updated on the server and updates on all clients.
If you have a large inbox, you can also specify to only pull down headers.
Allows you to specify a hierarchy of messages (Inbox/Business/Personal/Subscriptions/Contacts)
Post Office Protocol Version 3
Good if all you want to do is pull mail to a single client/computer. Is simple and works with everything. Runs faster on smaller inboxes.
If you have multiple clients, would have to mark emails marked as read in both clients.