You can retrieve your emails from your mail.com mailbox with a third party application. You decide when you want to retrieve your emails.
POP3 stands for "Post Office Protocol Version 3" and is a protocol for receiving email. This protocol enables offline mode. Emails are transmitted from a server to the email program you use and then deleted from the server, if not set otherwise. You then only have access to already retrieved and sent email through this email program. You can read emails which have already been downloaded without an Internet connection.
SMTP stands for "Simple Mail Transfer Protocol" and is a protocol for sending emails. SMTP transmits your emails from your email program to a server and then forwards them to the respective recipient.