A “Google proxy” refers to a specific type of “proxy server” which runs through Google applications. This allows a user to access websites without their personal IP (Internet Protocol) address being recorded by the website; Google’s own IP address will be recorded instead.
The function of a proxy server is to allow you to main more anonymous while visiting websites. Often, it will be undesirable for particular websites to have information relating to your IP address, which can potentially be used to identify your city, or even the street address of your Internet connection.
Using applications which are run through Google, it's possible to create a new proxy server using their “Create an application” tool. This may be preferable to other websites, as some dedicated proxy servers may only allow you to use their services for a short period of time before requiring a fee.
Using a proxy server does not ensure that you remain anonymous. Google will still retain information related to your use of the proxy server, and if necessary this information may be given to third parties.