This is a quick answer to a quick question. It just got useful enough to publish here.

Short answer:

pop3 if you have an intermitent internet connection, for example on the phone line as it was common years ago, where you would connect as if it was a phonecall so you would just fetch your emails quickly and then read them offline to free the line up for phonecalls.

You have the option to either leave your emails online, or delete them all (or after a few days – thunderbird gives you that option), so your emails may be both on your computer and online depending on what you decide. If you delete an email on Thunderbird it may still be on the server unless you’ve set it up to delete them all.

imap is more modern and appropriate when you have broadband. You are
continiously connected to the server and whatever you do on thunderbird, you are doing on the server – provided the connection is not interrupted. If you loose the connection, you loose access to the emails because you access them “on the server”. There are ways around this like syncronising but not particularly straight forward.

It is handy to access your emails from different computers in different places.