POP and IMAP are two protocols for using email with a mail client such as Windows Live Mail, Microsoft Outlook, or a mobile phone app.
POP stands for Post Office Protocol. If you use POP or POP3 as your mail protocol, by default all mail will download to the computer you are using to check your mail. If you check your mail from another computer, the webmail client, or your phone, there will be no messages to retrieve. This is an older protocol, but can be useful for backing up messages.
IMAP stands for Internet Message Access Protocol. If you use IMAP, all your email inboxes are in sync. If you read a message on your phone, your computer will show it as read shortly thereafter. If you delete an email from your computer, it will also be deleted from your phone’s mailbox as well. IMAP is the default protocol used by mobile phone email apps; if you are not given a choice of protocol, it will likely default to IMAP.