Google has allowed App marketers to use Google AdWords to click to download apps directly from the search ad. Now, with Google Play, Google AdWords would track the click, cost and if the user downloaded/installed the app on their device.
Now, Google added support to track if a user also downloaded/installed an iOS app. So now, if you spend money advertising your apps in AdWords, you should be able to see if it translates to someone downloading the app.
Well, not 100% of the time. If you are like me, you may download most your apps using iTunes and then sync your devices with iTunes to install the apps on those devices. In those cases, Google AdWords cannot track the download from the ad. They can only track it if you click the ad, and install the app from the device itself.
Why? Well, Google adds a tracking parameter that sees what device clicked on the app. Then if you add some code to your app, Google can then see if the device clicked on the ad. Then if they match, it can correlate the two. When done from a desktop and then synced later, Google cannot track it.
Google published this 45 minute help video on using Google Analytics with Apps, which may help some of you:
Forum discussion at WebmasterWorld.