They're all different email protocols (email "languages").
IMAP is the most popular for incoming emails, and offers 2-way syncing with your mail server.
POP (also called "POP3") is an older protocol for incoming emails, and only offers 1-way downloading of messages.
SMTP is the most common for outgoing (sending) emails.
Exchange/ActiveSync is proprietary to Microsoft Exchange (sometimes referred to as "Outlook"). ActiveSync is typically used by large organizations, and it handles both incoming and outgoing syncing.
Talkler currently supports IMAP, POP and SMTP.
Here's a helpful article from Yahoo with more info about MS Exchange, IMAP and POP.