A 3rd-party mail hosting provider handles all aspects of your domain's
email. You point your domain's MX records to their mail servers so that mail
sent to your domain goes directl to their servers.
They provide spam filtering and webmail.
They also provide POP and IMAP access to your mail as well as SMTP servers
that can be configured with local email clients like Outlook.
Using Google Apps for your domain, every account at your domain will have
access to the same Gmail webmail interface your users are used to with
their "@gmail.com" accounts.
However, all email sent and received will be for your domain name, not
for "@gmail.com"
You can also use Google Groups as mailing lists for your domain.