- POP:
All your email will be downloaded to the computer (into the mail client) and deleted from the mail server.
- IMAP:
When you read your email, the mail client will store the email on the mail server, and will manipulate it, and read it from the server. The email remains on the server, and you can access it via another IMAP mail client and view your mail exactly as it appears in your other IMAP client, which will keep everything in sync.