Think of Daydream as Cardboard, advanced edition. Available in the fall, Daydream will require a "newer" smartphone that meets the special to work with the Daydream software and app upgrades. One of the highlights is the VR integration within apps, like YouTube and Street View.
Be sure to check out the video below, a message from Google's Vice President of Virtual Reality, Clay Bavor. If you're interested, you can also find Google's entire I/O Keynote 2016 here.