Here is Quick Search Box description from Android Developers Blog
One of the new features we're really proud of in the Android 1.6 release is Quick Search Box for Android. This is our new system-wide search framework, which makes it possible for users to quickly and easily find what they're looking for, both on their devices and on the web. It suggests content on your device as you type, like apps, contacts, browser history, and music. It also offers results from the web search suggestions, local business listings, and other info from Google, such as stock quotes, weather, and flight status. All of this is available right from the home screen, by tapping on Quick Search Box (QSB).
What we're most excited about with this new feature is the ability for you, the developers, to leverage the QSB framework to provide quicker and easier access to the content inside your apps. Your apps can provide search suggestions that will surface to users in QSB alongside other search results and suggestions. This makes it possible for users to access your application's content from outside your application—for example, from the home screen.