IMAP and POP are different protocols that do similar things. Your observation is correct in that IMAP does provide better functionality than POP3.
The main differences in the two are that IMAP manages the email that's on the server, whereas POP3 downloads email from the server, leaving the client to manage the email locally.
Since IMAP leaves the email on the server and manages the email on the server (including folders), it's better suited for mailboxes that will be accessed by multiple users or from multiple locations.
Here's one tutorial for IMAP, http://www.opera.com/support/tutorials/mail/imap/
POP3 (POP=Post Office Protocol) is a protocol for client access to a mailbox. It downloads email from the mailbox and allows the client to manage the email internally.
SMTP is the common protocal for DELIVERING email, i.e. Simple Mail Transport Protocol. Clients send outbound email via SMTP, but they don't receive via SMTP, it's otherwise a Server-Server email transport protocol.