Basically, it works pretty much in the same way online banking or other login pages work. Using Secure Sockets Layer connections, the connection between you and Google is encrypted, so that third parties, beyond you and Google, cannot look at your search data.
"When you search on https://www.google.com, an encrypted connection is created between your browser and Google," said Evan Roseman, Software Engineer at Google, "This secured channel helps protect your search terms and your search results pages from being intercepted by a third party on your network. The service includes a modified logo to help indicate that you're searching using SSL and that you may encounter a somewhat different Google search experience."
It is important to note that this is a beta service, so for now, it only works with traditional search results - Google Maps or Google Image search is not yet supported, so switching to those results may take you out of your encrypted connection. It goes without saying that the encrypted connection may lead to slightly slower results; the search results in and of themselves are not affected.
To pre-empt any misunderstanding: encrypted search does not mean Google no longer stores your search data - it only means third parties cannot listen in to the connection between you and Google. "Searching over SSL doesn't reduce the data sent to Google - it only hides that data from third parties who seek it," Roseman explains.
Do any of you plan to use the encrypted version of Google?