This button redirects from the current page (http://example.com/page.html) to a URL where a proxy domain is appended to the host (http://example.com.proxy.u.edu/page.html). The proxy domain is set by the user at installation (default: ezproxy1.library.arizona.edu)
The redirect preserves the path, query and bookmark of the original page, so that http://example.com/dir/page.html?q=query#bookmark is redirected to http://example.com.proxy.u.edu/dir/page.html?q=query#bookmark
If you have the Google Toolbar installed, you can add this button by clicking here.
In order to access full texts of articles, I need to access the journal web site through the university library proxy. I simply got tired of typing in the 27 character long proxy domain in the address bar every time.
An alternative is to search through the proxy (using something like http://scholar.google.com.proxy.example.com), but I found that to be much slower at times (moreover, Google doesn't recognize your Google account this way).
This button was developed with the EZproxy web proxy server in mind (see also the Wikipedia article), but can be used whenever you want to switch from one domain to another while preserving the path, provided that the first domain is a prefix of the second one.
As Google Toolbar v3 has {url} and {url.host} variables, but not {url.path}, this redirect could not be done without using a script of some kind. Currently, it is implemented in PHP at my personal web site. All the code does is a redirect using header("Location: $redirect_url") based on the current URL and the set ezproxy domain. No information is collected whatsoever. The source code is accessible here.
Here is a bookmarklet that achieves the same thing. No privacy issues there, no server pinging (⇒ faster!). The JavaScript does it all on the client end.