This is a big one and foreshadows many of the rest of the changes. “Material design” refers to the new design guidelines for Android, Chrome, Google web apps, and any third-party apps on those platforms. This will be the first major UI update to Android since Ice Cream Sandwich (4.0), which introduced the “Holo” interface.
The idea here is that apps should give the impression of three dimensionality. If you are familiar with the cards interface of Google Now, for instance, you know that the cards are meant to be floating above the rest of the interface. Material design is about making things intuitive by focusing on vibrant colors, easily understood geometric shapes, and putting those things at different elevation levels.