Post Office Protocol is a simple mail protocol for getting a mail server to deliver your email to your machine. as such its suited for when you have a machine you use a lot and want to set up a mail client (Netscape Messenger, Outlook Express etc) to regularly check your mailbox.
POP style mail is convenient because once you've set up your mail program, it just gets your mail without additional fuss.
Interet Mail Access Protocol is a more featured protocol for email - the most obvious aspect of which is the ability to have multiple folders for organising your email. Mail generally lives on the mail server, instead of on your machine, so you can read it from wherever. webmail systems are generally based on IMAP maillboxes.
like POP, once you've set up an IMAP program, it'll remember all the details for you
the problem with POP-ing your mail is that you if you want to collect your mail from someone else's computer, you'd need to reconfigure their mail program to get your mail, and then change it back after and all sorts of nonsense like that.
webmail (like yahoo, hotmail etc) gets round this by whacking a web interface on your mailbox - so if you've got access to a web browser anywhere you can get your mail, all you need to remember is your
username and password.
so which are we using here?
all of them! i got peeved with having to use separate accounts depending where i was and what i was doing so i plugged all the bits together and this is the result - you can use whichever method suits you at the time. (edit: amazingly, such ubiquity was uncommon in 1998. Gmail didn't exist back then...)
however, since POP is simpler than IMAP (and so the webmail system too), there are somethings that POP can't do which the webmail can.
in particular, POP has no support for keeping separate folders. so if you use folders on the webmail system then you won't be able to see these when using POP.