A POP connection will cause your computer's mail program to download all your email, from the mail server and store the messages and the attachments on your computer. This is useful if you want to access your mail and attachments when you are not connected to the internet. Or if you do not want to pay for extra storage space on the server. If you choose this option, it is important that you also make sure your advanced settings delete the mail off the server after you download it. If you do not do this, your server will eventually become full of messages and attachments and your mailbox will run out of space. This will cause new mail to bounce until you delete your messages and free up space. Since you are downloading them anyways, there is no reason to keep them on the server. Unfortunately some mail programs do not force this option by default and it often causes problems for clients.
An IMAP connection allows you to view your mail from your mail program on multiple computers. This is handy if you have an office computer and a home computer or laptop and you want to sync all your messaging. The messages are not deleted from the server when they are downloaded to your computer. And you can specify whether or not you want them to messages and attachments to be stored on your computer for offline access. But even when you check your mail from one computer, you can still check it from another computer. You can also create folders on the account, which reside on the server, in order to organize your messages. And these folders will be accessible by all the computers that are accessing this account.
The disadvantage of IMAP is that it requires a lot of storage space on your server, so you need to let us know you plan on doing this, so that we can increase your mailbox from its default limit (200MB) to a higher limit, so that it doesn't run out of room and start bouncing messages. However, it's still a good idea to delete old attachments or remove the attachments once you no longer need access to them. This will help save space and reduce costs.