POP and IMAP are two protocols by which you are able to access/download emails from your mail server.
POP (Post Office Protocol) allows people to download copies of their email messages to their computer (provided the option to leave a copy of the mail message is enabled when setting up the account). If the option is not checked then the email itself is deleted from the mail server when it is downloaded to the computer. Any changes made to the mail message are only present on the computer on which the mail was downloaded and no one can see what changes were made and why.
IMAP (Internet Message Access Protocol) allows people to read emails as they arrive on the mail server. You are connected at all times to the mail server and any changes are visible to any one who log into that IMAP account. However if you are unable to connect to your mail server then the disadvantage of this protocol is that you are not able to read any emails (even those you downloaded via your email client like Outlook).
So which option should you choose?
You should based your answer based on the following options:
If you are the only person who is going to access/read all your emails then use POP otherwise use IMAP if multiple users are going to access the emails.
If you prefer to take backup of your emails yourself then use POP otherwise use IMAP.
If you are going to access your emails from one computer then use POP otherwise use IMAP if you access your emails from multiple computers/devices at multiple locations.
Hope the above helped you in understanding which option to choose and why.