Google Search puts the power of the search giant on your iPhone. It features everything you expect from the desktop version, plus image and voice search.
You can search the internet with Google using iOS's Safari browser, so why would you want a standalone Google Search App? Google's answer to that is to focus their app on the outside world, where you take your smartphone with you. This means voice and image search (Google Goggles).
Tap the microphone button, then say what you want to search for, and most of the time, Google Search will successfully search for what you said. This technology is surprisingly good - but not perfect. Image search is maybe even more impressive - it uses your camera to take a photo of something, and Google Search will then give you a list of pretty impressive results. It finds similar images, and most products are easily found so you can compare prices.
Google Search has an Apps button too - this leads you to the full suite of Google Apps, from Google Earth, to Picasa and Latitude. The user experience here is a bit mixed - some of these will open in Safari, others like Latitude will open the App store for a download. Hopefully at some point Google's suite of products will be better integrated into Google Search.
Google Search is an excellent search app, which proves its value as a standalone app. The access to other Google products seems a bit tacked on, but some users may find it useful.