Take a hotmail e-mail account versus a POP3 account you have on your account with RealWebs as an example.
With your hotmail account, you cannot use an external e-mail client to check for new messages or send outgoing messages. Instead, you must visit the hotmail website, log into your account in order to perform these functions. In the meantime, you are subjected to advertisements, and the process is restricted to a web-interface.
On the other hand, your POP3 accounts are accessible from any compatible e-mail client. This allows for added functionality on your side (such as the ability to check for new messages every so often, create filters, etc.).
If you prefer a web-based e-mail system, you can access the eMail in your account by going to:
http://email.mydomain.tld <-- replace mydomain.tld with your domain name.