In other words, what this feature does is to suggest things to listen to while driving, including music, podcasts, and even news powered by Google News.
When tapped, the button launches a dedicated new UI that uses the entire screen, with large thumbnails to let you easily choose content to listen to. A single tap on any of the thumbnails is enough to begin playing, and you can also revert to the previous screen by tapping the button again.
Worth knowing is this feature isn’t yet available for everybody out there running Android Auto, and most likely, it’s powered by a server-side switch. This means the suggested media feature is still in the experimental phase and Google just slowly rolls it out to users out there in an attempt to determine its overall reliability before bringing it to everyone.
The Android Auto version that you are running doesn’t make any difference, given Google itself decides who gets the new button and who doesn’t. Someone claims they’re running Android Auto 6.6, so it’s not the latest version of the app, and they still got the suggested media feature.
Unfortunately, this new button doesn’t seem to come with a dedicated setting to turn it off, so if you don’t find it useful, there’s no way to get rid of it. It remains to be seen if Google introduces such settings by the time the general availability is reached though.