Analogy time!
POP is like a post office box. If the iPhone goes and gets mail first and takes it to its home, the computer will no get any of that mail but will get any new mail that arrived since the last time the iPhone was there. Its like the wife going to the post office mid-day and getting all the mail, the husband will find none later after work. You do not need to open it to take it.
IMAP is sorts like a mirror. The mail stays at the post office, yet many people can view the same stuff anywhere. What they see though is a reflection of what is there. The nice thing is everyhing is synced. If one person deletes something, it affects all. New messages work the same way and once marked read, everyone sees it was read. No need to read the bills twice!