I have a web server that runs my web application.
If I want to outsource my email to another provider, is it possible if they are on their on network/data center?
Yes. To do this, you will need access to the DNS records for your domain. The MX record allows you to set up a mail server that's separate from the web server.
Google offers a service that will manage your domain's email through GMail, and the instructions on how to reconfigure your DNS for this service can be found here.