Drawer
The old default navigation mode from 3.5 and earlier. There is a "hamburger" menu in the top right that opens up a drawer menu on the left hand side. From there you choose the view to navigate to.
Tabs
This is similar to the GMMP 2.x Holo theme's navigation mode. There is a navigation bar at the top with a bunch of tabs. The bar is scrollable left/right and all the options/settings are accessible from the 3 dot menu at the top right. Tab navigation has an optional search button available to toggle in the customize menu.
Bottom
The default navigation mode for 3.6+. Bottom navigation has 5 "top" level areas. Library, Queue, Search, Effects, and Settings. Each one has its own navigation backstack, so you can search for something in the search view and then jump back to the library view to whatever you were looking at previously.