Google mobile app is google’s first native application for IPhone and IPod touch which emphasis on providing a better search experience on mobile.
From Google Mobile Blog
Google Mobile App gives you a single text box to search through your contacts and the web. As soon as you start typing, it scours Google for things to help you. These could be typing suggestions, website suggestions or easy access to a search you made before. Google Mobile App even searches as you type so that you see results as soon as you finish typing. Over time, the App remembers the things you do most and puts them at the top. Finally, Google Mobile App also uses the My Location feature to detect your current location and show nearby businesses on a map.
Let’s see it in action in this video: