For students and teachers the most notable aspect of the new version is a streamlined integration of Street View and 3D Earth View imagery. The new version of Google Maps will have an image carousel that you can open at the bottom of your screen. That carousel will allow you to quickly zoom to a Street View or Earth View complete with 3D imagery. This appears to eliminate the need for the Google Earth Browser Plug-in if you're using Chrome.
One of the new features of Maps that Google is touting most highly is improved discovery of places of interest near locations that you click on the map. Another new feature is the option to compare routes between places based upon the mode of transportation you intend to use.
The new version of Google Maps is still in beta. You can register for an invitation to be a beta user here. Learn more about the new Google Maps in the video below.
Update: TechCrunch posted an informative video featuring a live walk-through of the new Google Maps.