If you wish to use Google's Mail service instead of having mail routed through our servers, you need to sign up for Google Apps at http://www.google.com/apps/
Once you've done that you need to change your MX Entry in your cPanel.
Start by setting the email routing to 'Remote Mail Exchanger'. This tells the server that all of your mail will be routed via an external mail server.
Next, remove any MX entries present.
Finally enter in the following priorities and destinations...
10 ASPMX.L.GOOGLE.COM.
20 ALT1.ASPMX.L.GOOGLE.COM.
21 ALT2.ASPMX.L.GOOGLE.COM.
30 ASPMX2.GOOGLEMAIL.COM.
31 ASPMX3.GOOGLEMAIL.COM.
32 ASPMX4.GOOGLEMAIL.COM.
33 ASPMX5.GOOGLEMAIL.COM.